Ordinary Limits Research Articles

On lax limits in ∞-categories

We introduce partially lax limits of ∞ \infty -categories, which interpolate between ordinary limits and lax limits. Most naturally occurring examples of lax limits are only partially lax; we give examples arising from enriched ∞ \infty -categories and ∞ \infty -operads. Our main result is a formula for partially lax limits and colimits in terms of the Grothendieck construction. This generalizes a formula of Lurie for ordinary limits and of Gepner, Haugseng, and Nikolaus for fully lax limits.

Approximate injectivity and smallness in metric-enriched categories

Properties of categories enriched over the category of metric spaces are investigated and applied to a study of well-known constructions of metric and Banach spaces . We prove e.g. that weighted limits and colimits exist in a metric-enriched category iff ordinary limits and colimits exist and ε -(co)equalizers are given by ε -(co)isometries for all ε . An object is called approximately injective w.r.t. a morphism h : A → A ′ iff morphisms from A into it are arbitrarily close to those morphisms that factorize through h . We investigate classes of objects specified by their approximate injectivity w.r.t. given morphisms. They are called approximate-injectivity classes. And we also study, conversely, classes of morphisms specified by the property that certain objects are approximately injective w.r.t. them. For every class of morphisms satisfying a mild smallness condition we prove that the corresponding approximate-injectivity class is weakly reflective, and we study the properties of the reflection morphisms. As an application we present a new categorical proof of the essential uniqueness of the Gurarii space.

Light Cones as Quantum Phenomena

Quantum erasure experiments push the boundary between the quantum and classical worlds by letting delayed events influence the state of previously recorded and potentially widely distributed classical information. The only significant restriction to such unsettling violations of forward-only causality is that the distribution of forward-dependent information cannot cross out of the light cone boundaries of the event in the past, a feature that ensures no violations of causality — no rewriting of anyone else's recorded histories — can occur. The erasure interpretation of this conundrum requires rewriting of information recorded and distributed in the past, which would itself be a violation of causality. The quantum predestination interpretation removes the causal rewriting issue. However, quantum predestination requires detailed coordination of inputs from outside of the forward-dependent event's light cone, thus massively violating the same limit that prevents causality violations in such events. Yet another approach is to invoke the Schrödinger's cat variant of quantum erasure in which arbitrarily complex classical events within the light cone become quantum dependent upon the future event. As with all Schrödinger's cat interpretations of quantum mechanics, this variant of quantum erasure violates causality by discarding local classical histories such as the information-rich state of the cat's body. The most straightforward interpretation of erasure experiments is to follow the lead of the equations themselves, which transform on paper as if their components are independent of ordinary space and time limits, up to the limits imposed on them by the speed of light. Interpreting the light cone of each quantum system as an atemporal, aspatial unit in which classical time and space have no meaning results in a multi-scale, matter-dependent definition of spacetime in which every light cone is a singular quantum entity. In such a universe, both time and space are defined not as pre-existing, mass-independent continuums but as the consensus of vast numbers of constantly interacting and mutually limiting quantum-entity light cones.

Weighted limits in an $$(\infty ,1)$$-category

We introduce the notion of weighted limit in an arbitrary quasi-category, suitably generalizing ordinary limits in a quasi-category, and classical weighted limits in an ordinary category. This is accomplished by generalizing Joyal’s approach: we identify a meaningful construction for the quasi-category of weighted cones over a diagram in a quasi-category, whose terminal object is the weighted limit of the considered diagram. We then show that each weighted limit can be expressed as an ordinary limit. When the quasi-category arises as the homotopy coherent nerve of a category enriched over Kan complexes, we generalize an argument by Riehl-Verity to show that the weighted limit agrees with the homotopy weighted limit in the sense of enriched category theory, for which explicit constructions are available. When the quasi-category is complete, tensored and cotensored over the quasi-category of spaces, we discuss a possible comparison of our definition of weighted limit with the approach by Gepner-Haugseng-Nikolaus.

Taboo and capitalism: Of incest, YouTube and profanation in contemporary capitalism

Taboo, as a space where the prohibited resides, delimits the form of the thinkable in a society. Freud, in Totem and Taboo, attempted to trace an explanation beyond the ‘categorical imperative’ of morality and custom. A century later the YouTuber PrankInvasion (Chris Monroe) seems to continue Freud’s account to his advantage. Through ‘Kissing my actual sister prank’, one of his most controversial videos, he challenged his own followers to fulfil an especially controversial challenge: kiss his own stepsister. It is through these contacts with the limits of the moral, of the acceptable, that capitalism expands the colonized territory, absorbing the profane under its new exposure value. The unthinkable, the purported profanation of dogma (in this case, taboo of incest), disappears under the standardization of all rites as standardized consumable objects. But as Agamben warns about the nature of desecration it can not be related, in its new use, with the consumption realm. And that is not the case with PrankInvasion. Through the apparent absence of ordinary moral limits, Chris Monroe expresses his heartfelt attachment to the most extraordinary limit of capitalism: economic growth.

Self-Enforcing Legal Limits: Bureaucratic Constraints on Repression under Emergency Powers

Governments of all stripes have attempted to transgress ordinary legal limits and infringe upon rights and liberties under the cover of emergency powers. Are repressive policies adopted under emerg...

On the ideal convergence of sequences of Świątkowski functions

For any Borel ideal $$\mathscr {I}$$ the class of $$\mathscr {I}$$ -limits of sequences of Świątkowski functions is described. In particular, we characterize Borel ideals $$\mathscr {I}$$ for which classes of ideal and ordinary limits of sequences of Świątkowski functions coincide. We consider also ideal limits of sequences of functions possessing the Świątkowski property related to some density-type topologies. Moreover, an alternative characterization of ordinary limits of sequences of Świątkowski functions is given.

Montaigne in Transit: Essays in Honour of Ian Maclean . Edited by N eil K enny , R ichard S cholar , and W es W illiams Montaigne in Transit: Essays in Honour of Ian Maclean . Edited by KennyNeil, ScholarRichard, and WilliamsWes. Oxford: Legenda, 2016. 282 pp.

This is an impressive collection of essays by Ian Maclean’s colleagues and students, a future landmark study like Ian Maclean and I. D. McFarlane’s earlier edited book, Montaigne: Essays in Memory of Richard Sayce (Oxford: Clarendon Press, 1982). The book grew out of a series of meetings of contributors, and this has produced an exceptionally well conceived and coherent collection. It focuses on the creation and consumption of the Essais through two pairs of critical concepts — genesis and production, and diffusion and reception — which the contributors explore and question, offering a subtle and complicated view of book and reception history and rethinking the ordinary limits of intertextuality in the process. Chapters examine how the Essais move forwards and backwards in time, how they anticipate and rewrite themes and commonplaces, and how they continue to speak to readers today. The book’s theme, defined by the editors in their Introduction as ‘the “transit” of [Montaigne’s] work through time, space, language, discipline, and genre’ (p. 2), builds on important work on movement in the Essais, while allowing time and space for innovative and varied methodologies and techniques of reading, from Terence Cave’s cognitive criticism (deployed to explore how Montaigne’s embodied thought is enacted on the page) to Warren Boutcher’s division of ‘Des cannibales’ into rhetorical periods, showing the shape of Montaigne’s Ciceronian training more clearly to unversed modern readers. Intertextuality is persuasively re-imagined as influence, buried or explicit, in many of the chapters: Rowan Tomlinson on Angelo Poliziano’s eclectic humanism and its overlooked undertow; Kathy Eden on Erasmus’s rhetoric of the face; and Emma Herdman on the provocations and pleasures of Juvenal for women readers. Other chapters explore the effects and mutations of the Essais over time: Kate Tunstall on the power of the will and of the imagination in Diderot, Montaigne, and Augustine; and Timothy Chesters on Flaubert’s reading of the Journal de voyage. A real strength of the collection is its geographical reach, covering responses to the Essais in Germany and Britain: Valerie Worth-Stylianou on the treatment of Montaigne’s Latin quotations by his English translator, John Florio, and his French editor, Marie de Gournay; John O’Brien on Christoph Besold’s reading of the Essais as part of a shared intellectual and legal tradition; Ingrid De Smet on Isaac D’Israeli’s reading of Montaigne, refracted through translations, collections of ana, and compilations; Kathryn Murphy on Montaigne and Robert Burton’s shared interest in the particular; and Colin Barrow on Montaignian moments of reflection and the performance of thought in Shakespeare. Others offer a thematic focus, exploring the flexibility of a theme and how it is turned over and inside out in the Essais’s meandering progress: Chimène Bateman on how marriage is questioned and problematized; and Frank Lestringant on the shifts and mingling of vanity, travel, and writing. As Ian Maclean points out in his Afterword, many of these contributions feature the ‘triangulation’ of the Essais with a reader and a shared antecedent (p. 259), fracturing the familiar story of sources and intertexts. This rich and rigorous collection is a proud tribute to the different directions and approaches inspired by Ian Maclean’s work, and a valuable addition to Montaigne and early modern studies.

Mahavier completeness and classifying diagrams

Generalised inverse limits of compacta were introduced by Ingram and Mahavier in 2006. The main difference between ordinary inverse limits and their generalised cousins is that the former concerns diagrams of singlevalued functions while the latter permits multivalued functions. However, generalised inverse limits are not merely limits in the Kleisli category of a hyperspace monad, a fact that independently motivated each of the authors of this article to come up with the same formalism which restores the link with category theory through the concept of Mahavier limit of an order diagram in an order extension of a category B . Mahavier limits of diagrams in B coincide with ordinary limits in B , and so Mahavier limits are an extension of ordinary limits along the functor that views an ordinary diagram as a diagram in the extension. Within that context it is natural to consider Mahavier completeness, namely when all small diagrams admit Mahavier limits, as well as classifying diagrams, namely the existence of a right adjoint to the mentioned functor on diagrams. In this work we show that these two conditions are equivalent, and we study some of the properties of classifying diagrams and of the adjunction.

Gastos públicos: análise da aplicacão da Lei de Responsabilidade Fiscal e da Constituição Federal no COREDE Alto Jacuí

Planning and public spending control are one of the most important parts of the new regime in public administration. In this context, the objective of this work is to analyze the limits established by the Fiscal Responsibility Law (LRF) and Federal Constitution at COREDE Alto Jacuí from 2005 to 2008. The analyses have indicated that the LRF is not being applied in all the cities in this study due to the fact that the ordinary and integral legal limits established have not been applied. Furthermore, it could be observed that the value spent with salaries has grown continually during the period analyzed, mainly in cities with less population and economically smaller. Although the limits invested in education and health are according to the percentage in law, the majority of the cities in this study have shown contrasting results, and many cities with similar structure have had different results considering the areas studied, leading to the conclusion that heterogeneity in terms of size (populations and taxes collected) may be not a determinant observed factor in the legal limits.

The Ordinary and Extraordinary: Producing Migrant Inclusion and Exclusion in US Sanctuary Movements

This article analyzes the Sanctuary Movement for Central Americans and the New Sanctuary Movement, two United States faith-based social movements, to think through the ways in which these pro-immigrant efforts paradoxically render migrants figuratively mute and often excluded from conceptualizations of the nation and its inhabitants even as they advocate for legal inclusion. We examine this tension of inclusion and exclusion through the frequent representation of migrants’ histories and Christianity as extraordinary in the Sanctuary Movement for Central Americans, and migrants’ lives as ordinary in the New Sanctuary Movement. We identify two key processes by which this framing of migrants as extraordinary or ordinary limits the enactment of full social, political, and economic inclusion: (a) public support is principally granted to certain stories, religions, identities, and experiences; and (b) migrants are consistently positioned, and often celebrated, by sanctuary activists as “others.” The discourses of migrants as extraordinary or ordinary effectively generate broad involvement of faith communities in sanctuary work. Yet, as we argue, this framing comes with the cost of limiting activist support only to particular groups of migrants, flattening the performances of migrant identities, and positioning migrants as perpetually exterior to the US. Reliance on discourses of the extraordinary and ordinary, therefore, can truncate opportunities for making legible a range of migration experiences and extending belonging to all migrants, outcomes that arise in contrast to the purported inclusionary goals of the faith-based sanctuary social movements.

On Some Founding Ideas of Quailology and Their Propounders

Powerful ideas in quailology affect thinking over generations, even if the ideas are wrong. I discuss great ideas put forth by Aldo Leopold, Herbert Lee Stoddard, and Paul Lester Errington and comment on aspects of their personalities. Leopold, an extraordinarily good father, posited the Law of Dispersion (Interspersion), which became known as the Principle of Edge. The Law is a tautology that can be paraphrased ‘edge-obligate animals require edge.’ Leopold observed the ‘law’ held ‘within ordinary limits,’ which he did not define but which could mean ‘within compositionally simple landscapes.’ As a child, Stoddard, who dropped out of high school to support his family, recognized the value of fire in northern bobwhite (Colinus virginianus) habitat management in the Southeast; later he came to see tenant farming (patchwork agriculture) set up conditions favorable to northern bobwhites. Stoddard was given to after- the-fact hypothesis formulation (retroduction) on the causes of events he observed. Through this logically weak process he bequeathed many ‘facts’ that are really untested hypotheses. Errington, an apparent loner who survived polio as a child, had 2 great ideas. The Threshold of Security was a fairly constant spring density which implied harvest up to a certain level is fully compensatory (doomed- surplus model). The Principle of Inversity implies that relative productivity declines as breeding density increases. Errington’s own work refuted the doomed-surplus model because he could not have simultaneously observed a constant breeding population and inversity, which requires a variable breeding population. These great founding ideas, although not without flaw, arose through observation of nature and thought, not through null hypothesis significance testing and model selection.

What’s in a Nym? Gender, Race, Pseudonymity, and the Imagining of the Online Persona

What’s in a Nym? Gender, Race, Pseudonymity, and the Imagining of the Online Persona

Generalized limits and related asymptotic formulas

On the basis of the new version of Karamata’s theorem, stated in terms of generalized limits, we succeed in weakening the conditions of validity of the Connes asymptotic formulas studied by many authors. Using this approach, we can apply the criterion of “measurability” due to Connes for passing from generalized limits to ordinary limits.

A Group Analytic Understanding of the Tour de France: Why the Fittest Rider Does Not Necessarily Win

This article recognizes that sports coaching uses predominantly cognitive-based psychological techniques to bring about success. On the whole a psychoanalytic application to sporting success is minimal. Athletic success at the highest level requires suffering beyond the ordinary limits we would expect individuals to endure. In my experience psychoanalysis de-contextualises suffering in sport so that it is seen as a form of self-harm. This position limits the scope of psychoanalytic understanding to support professional athletes in maximising their athletic potential. This article is especially interested in how group analytic theory can be applied to create a winning identity. The theatre of operation in which this identity formation will be tested is the Tour de France (bicycle race).

Restriction categories III: colimits, partial limits and extensivity

A restriction category is an abstract formulation for a category of partial maps, defined in terms of certain specified idempotents called the restriction idempotents. All categories of partial maps are restriction categories; conversely, a restriction category is a category of partial maps if and only if the restriction idempotents split. Restriction categories facilitate reasoning about partial maps as they have a purely algebraic formulation.In this paper we consider colimits and limits in restriction categories. As the notion of restriction category is not self-dual, we should not expect colimits and limits in restriction categories to behave in the same manner. The notion of colimit in the restriction context is quite straightforward, but limits are more delicate. The suitable notion of limit turns out to be a kind of lax limit, satisfying certain extra properties.Of particular interest is the behaviour of the coproduct, both by itself and with respect to partial products. We explore various conditions under which the coproducts are ‘extensive’ in the sense that the total category (of the related partial map category) becomes an extensive category. When partial limits are present, they become ordinary limits in the total category. Thus, when the coproducts are extensive we obtain as the total category a lextensive category. This provides, in particular, a description of the extensive completion of a distributive category.

This strange illness: alcoholism and Bill W

brilliant work, both personal and professional in character, is a study of alcoholism, of a movement aimed at its cure, and of an individual participant in this development. The author develops an interlinked theory and scientific research program that describe an illness of the mind, body, and spirit. He does so without allowing the assumptions underlying the way we look at one area of illness, say the mind, to contradict the assumptions underlying the way we look at the human body or for that matter the human spirit. That Lobdell carries this project to a successful conclusion makes this a compelling work for everyone in the field of alcohol studies and social pathology. Lobdell, who has written on a broad range of subjects, here argues the originality and importance of recognition of alcoholism a tripartite illness, and of congruent treatment for the three parts. He thus accepts a medical view of this vast social problem, but also recognizes dimensions within it that go beyond the ordinary limits of medical practice, well the complexity of its treatment. His book is at once an intellectual history of Bill W.'s vision; a short history of alcohol addiction and the culture of that addiction; a treatise on the psychological, biochemical, and spiritual aspects of the illness and its treatment; and a scientific research program for the future. Norman K. Denzin of the University of Illinois has hailed the book as a wonderful story brought to a sophisticated readership, and will widely appeal to the recovering population. Matthew J. Raphael, intimate with the subjects well the concerns of this book says, This Strange Illness is an astounding book. Jared Lobdell, a brilliant polymath, traverses a spectrum of disciplines u from biogenetics and chaos theory to psychology, sociology, and theology u in search of a sufficiently complex and comprehensive understanding alcoholism. is the most intellectually rigorous study I have ever seen in the field. Jared C. Lobdell is author or editor of a dozen books in history and criticism and a number of articles in fields ranging from alcohol studies to systems analysis. He has served a fellow at the Center for Alcoholism and Addiction Studies, Brown University. His current positions are at Millersville University of Pennsylvania and adjunct professor at Elizabethtown College in Pennsylvania.

Poetry in the boardroom: thinking beyond the facts

PurposeTo convey the findings of an investigation into the relationship between poetry and business thinking, which began with the hypothesis that regular reading and analysis of poetry and its levels of meaning, subtle verbal and nonverbal contextual nuances, emotional content, and required associative thinking will help people deal with ambiguity, delay closure on decisions, and result in more systemic thinking and in better business decisions.FindingsThe research and workshops indicate that reading poetry can expand thinking space by enhancing associative thinking and access to preconceptual areas.Research limitation/implicationsThe findings are based on extensive interdisciplinary research and a small number of seminars and workshops. No formal studies have yet been conducted.Practical implicationsThis provides a way to open thinking spaces that may be often unused by the business strategist, and that can lead to better decisions. By focusing on how executives can refine their thinking abilities to take them beyond the ordinary limits of cause‐and‐effect approaches, encourages the application of those radical judgments that can help differentiate one organization from another.Originality/valueThe authors believe they are the first to explore this relationship between reading poetry and business thinking.

The Legacy of Bobwhite Research in South Texas

More than a half century of research on northern bobwhites (Colinus virginianus) in south Texas has provided a legacy of information for ecologists and managers. South Texas is a semiarid and subtropical environment with highly variable weather, a land base consisting of large private ranches devoted to livestock production, a perennial problem of brush encroachment on rangelands, and a strong tradition of fee-lease hunting. These physical, biotic, and social conditions focused research efforts on descriptive natural history (ca. 1930-1980) and evaluation of grazing and brush management practices (ca. 1980-1990). By natural evolution of knowledge, these efforts led to the development of unified theory that synthesized descriptive and applied information about bobwhite management (ca. 1990-2000). In the context of grazing on rangeland subject to encroachment by woody plants, descriptive studies focused on bobwhite home ranges, mobility, flight behavior, nesting cover, resting cover, and whistling posts, among other aspects of habitat use and behavior. The purpose of these studies was to determine how different plant structures and communities should be dispersed in space and time to maximize their value as bobwhite habitat. South Texas studies revealed that the dogmatic principle, bobwhites are early successional species, holds poorly in semiarid, subtropical environments. Research in south Texas led to formalization of the usable-space-in-time hypothesis on bobwhite density. The hypothesis states that, within ordinary limits, mean abundance of bobwhites on an area is correlated more strongly with the quantity of permanent cover to which they are adapted and less strongly with (human) perceptions of habitat quality (foods, interspersion, edge, diversity). Space-time seems to be an omnibus variable that can be assessed in a variety of management and ecological settings. In association with highly variable rainfall patterns and amounts in south Texas, bobwhite populations exhibit boom-bust population behavior. Research on the cause-effect process governing booms and busts has led to rejection of hypotheses on phosphorus, calcium, phytoestrogens, vitamin A, macronutrition, water, and stress-related hormones as causally involved in the phenomenon. Heat-mediated variation in productivity remains a viable hypothesis that is, of course, open to challenge. The information legacy from research on bobwhites in south Texas has led to revision of knowledge emanating from the southeastern United States; the revised knowledge better fits bobwhites and other quails that inhabit semiarid environments.

Three Phases of Treatment with Borderline and Psychotic Patients

Three distinct, yet overlapping, phases of treatment emerge when working with some borderline and psychotic patients. This are patients who test the ordinary limits of psychoanalysis, but can profit from its deep exploration. The first phase is colored by acting out, interpersonally and intrapsychically. An analytic envelope of containment is necessary to sustain the treatment. Interpretive holding and containing help the patient find a psychic receptacle capable of detoxifying violent projections. Many of these patients terminate prematurely. The second phase is centered around the patient's defensive use of the death instinct to extinguish or destroy certain parts of their mental functioning. This difficult standoff between parts of the patient's mind becomes replicated in the transference. The third phase reveals the more fundamental problem of paranoid∼schizoid anxieties of loss and primitive experiences of guilt. These include fears of persecution and annihilation. Some patients abort treatment in the first or second phase and never work through the phantasies and feelings of loss. Nevertheless, much intrapsychic and interpersonal progress is possible. Given the instability and chaotic nature of these patient's object relations, the analyst must be cautiously optimistic in their work and realize the potential to help the patient even when presented with less than optimal working conditions.