Category Of Complexes Research Articles

NHC Core Phosphonium Ylide-based Palladium(II) Pincer Complexes: The Second Ylide Extremity Makes the Difference.

The coordinating properties of N-heterocyclic carbene (NHC) (A), phenolate (B), and phosphonium ylide (C) moieties were investigated systematically through the preparation of a family of NHC, phosphonium ylide-based pincer ligands, where the third donor extremity can be either an NHC, a phenolate, or a phosphonium ylide. The overall donor character of such ligands [NHC(AaBbCc)] (a + b + c = 2) was analyzed by comparison of the molecular orbitals (energy and shape), oxidation potentials (Epox), and IR νCO and νCN stretching frequencies of their isostructural pincer Pd(II) complexes [NHC(AaBbCc)PdL][OTf] (L = NCCH3, CO, or CNtBu). The three categories of pincer complexes based on phosphonium ylides were easily obtained by acidic treatment of their highly stable ortho-metalated Pd(II) precursors prepared in a single step from readily available N-phosphonio-substituted imidazolium salts. Analysis of IR data indicated that NHC and phenolate ligands have a similar donor character but which remains lower than that of the phosphonium ylide. The impact on catalytic performance of the incorporation of a second strongly donating phosphonium ylide into the ligand architecture was illustrated in the Pd-catalyzed allylation of aldehydes.

The weight complex functor is symmetric monoidal

Bondarko's (strong) weight complex functor is a triangulated functor from Voevodsky's triangulated category of motives to the homotopy category of chain complexes of classical Chow motives. Its construction is valid for any dg enhanced triangulated category equipped with a weight structure. In this paper we consider weight complex functors in the setting of stable symmetric monoidal ∞-categories. We prove that the weight complex functor is symmetric monoidal under a natural compatibility assumption. To prove this result, we develop additive and stable symmetric monoidal variants of the ∞-categorical Yoneda embedding, which may be of independent interest.

Completing perfect complexes

This note proposes a new method to complete a triangulated category, which is based on the notion of a Cauchy sequence. We apply this to categories of perfect complexes. It is shown that the bounded derived category of finitely presented modules over a right coherent ring is the completion of the category of perfect complexes. The result extends to non-affine noetherian schemes and gives rise to a direct construction of the singularity category. The parallel theory of completion for abelian categories is compatible with the completion of derived categories. There are three appendices. The first one by Tobias Barthel discusses the completion of perfect complexes for ring spectra. The second one by Tobias Barthel and Henning Krause refines for a separated noetherian scheme the description of the bounded derived category of coherent sheaves as a completion. The final appendix by Bernhard Keller introduces the concept of a morphic enhancement for triangulated categories and provides a foundation for completing a triangulated category.

Matlis category equivalences for a ring epimorphism

Under mild assumptions, we construct the two Matlis additive category equivalences for an associative ring epimorphism u:R⟶U. Assuming that the ring epimorphism is homological of flat/projective dimension 1, we discuss the abelian categories of u-comodules and u-contramodules and construct the recollement of unbounded derived categories of R-modules, U-modules, and complexes of R-modules with u-co/contramodule cohomology. Further assumptions allow to describe the third category in the recollement as the unbounded derived category of the abelian categories of u-comodules and u-contramodules. For commutative rings, we also prove that any homological epimorphism of projective dimension 1 is flat. Injectivity of the map u is not required.

Functoriality of Khovanov homology

In this paper, we prove that every Khovanov homology associated to a Frobenius algebra of rank 2 can be modified in such a way as to produce a TQFT on oriented links, that is a monoidal functor from the category of cobordisms of oriented links to the homotopy category of complexes.

LOCAL DUALITY FOR THE SINGULARITY CATEGORY OF A FINITE DIMENSIONAL GORENSTEIN ALGEBRA

A duality theorem for the singularity category of a finite dimensional Gorenstein algebra is proved. It complements a duality on the category of perfect complexes, discovered by Happel. One of its consequences is an analogue of Serre duality, and the existence of Auslander–Reiten triangles for the$\mathfrak{p}$-local and$\mathfrak{p}$-torsion subcategories of the derived category, for each homogeneous prime ideal$\mathfrak{p}$arising from the action of a commutative ring via Hochschild cohomology.

Allylic hydrocarbon polymers complexed with Fe(II)(salen) as a ultrahigh oxygen-scavenging and active packaging film

Abstract Macromolecular metal complexes provide a molecular-based synergy function of organic polymers and combined metal complexes. A new category of macromolecular complexes includes catalytically active metal complexes immobilized by organic polymers containing reactive substrate moieties in their repeating units. Here, we describe the extremely efficient oxidation of allylic hydrocarbon polymers with the attached iron complex catalyst, as well as the efficient oxygen-consumption or oxygen-scavenging function of the matrix polymer film. The less toxic N,N´-di(salicylaldehyde)ethylenediiminatoiron(II) complex was combined with or fixed onto a series of allylic hydrocarbon polymers as both the oxidative substrate and the film matrix, i.e. poly(1,2-butadiene), polynorbornene, poly(5-vinyl-2-norbornene), poly(2,5-norboenadiene), poly(dicyclopentadiene), and poly(5-ethylidene-2-norbornene). Ultra-high oxygen-scavenging capacity up to 300 mL (oxygen gas at STP)/g(film) was achieved, based on the oxidative consumption of the allylic bond (particularly of poly(5-ethylidene-2-norbornene)), which was more than three times that of the previously reported highest oxygen-scavenging polymers. These oxygen-scavenging films are based on the high reactivity of polymer-metal complexes that provides an innovative development in the area of active packaging polymer films that facilitate cost-effective performance, safety, and sustainability.

Finite-dimensional differential graded algebras and their geometric realizations

We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with a full separable semi-exceptional collection. Moreover, we also show that it gives a characterization of such categories assuming that a subcategory is idempotent complete and has a classical generator.

Intersection Space Constructible Complexes

We present an obstruction theoretic inductive construction of intersection space pairs, which generalizes Banagl's construction of intersection spaces for arbitraty depth stratifications. We construct intersection space pairs for pseudomanifolds with compatible trivial structures at the link fibrations; this includes the case of toric varieties. We define intersection space complexes in an axiomatic way, similar to Goresky-McPherson axioms for intersection cohomology. We prove that if the intersection space pair exists, then the pseudomanifold has an intersection space complex whose hypercohomology recovers the cohomology of the intersection space pair. We characterize existence and uniqueness of intersection space complexes in terms of the derived category of constructible complexes. In the case of algebraic varieties we show that a parallel obstruction theory in the derived category of Mixed Hodge Modules endowes intersection space cohomology with a Mixed Hodge Structure if the obstruction vanishes. We find classes of examples admitting intersection space complex, and counterexamples not admitting them which illustrate the use of the previously developed obstruction theory (counterexamples were known previously by various specialists). We prove that the (shifted) Verdier dual of an intersection space complex is an intersection space complex. We prove a generic Poincaré duality theorem for intersection space complexes.

Cotorsion pairs and adjoint functors in the homotopy category of N-complexes

In this paper, we first construct some complete cotorsion pairs on the category [Formula: see text] of unbounded [Formula: see text]-complexes of Grothendieck category [Formula: see text], from two given cotorsion pairs in [Formula: see text]. Next, as an application, we focus on particular homotopy categories and the existence of adjoint functors between them. These are an [Formula: see text]-complex version of the results that were shown by Neeman in the category of ordinary complexes.

Pyramids and 2-representations

We describe a diagrammatic procedure which lifts strict monoidal actions from additive categories to categories of complexes avoiding any use of direct sums. As an application, we prove that every simple transitive 2-representation of the 2-category of projective bimodules over a finite dimensional algebra is equivalent to a cell 2-representation.

Model categories of quiver representations

Gillespie's Theorem gives a systematic way to construct model category structures on C(M), the category of chain complexes over an abelian category M.We can view C(M) as the category of representations of the quiver ⋯→2→1→0→−1→−2→⋯ with the relations that two consecutive arrows compose to 0. This is a self-injective quiver with relations, and we generalise Gillespie's Theorem to other such quivers with relations. There is a large family of these, and following Iyama and Minamoto, their representations can be viewed as generalised chain complexes.Our result gives a systematic way to construct model category structures on many categories. This includes the category of N-periodic chain complexes, the category of N-complexes where ∂N=0, and the category of representations of the repetitive quiver ZAn with mesh relations.

Minimal Generators of Hall Algebras of 1-cyclic Perfect Complexes

AbstractLet $A$ be the path algebra of a Dynkin quiver over a finite field, and let $C_1(\mathscr{P})$ be the category of 1-cyclic complexes of projective $A$-modules. In the present paper, we give a PBW-basis and a minimal set of generators for the Hall algebra ${\mathcal{H}}\,(C_1(\mathscr{P}))$ of $C_1(\mathscr{P})$. Using this PBW-basis, we firstly prove the degenerate Hall algebra of $C_1(\mathscr{P})$ is the universal enveloping algebra of the Lie algebra spanned by all indecomposable objects. Secondly, we calculate the relations among the generators in ${\mathcal{H}}\,(C_1(\mathscr{P}))$, and obtain quantum Serre relations in a quotient of certain twisted version of ${\mathcal{H}}\,(C_1(\mathscr{P}))$. Moreover, we establish relations between the degenerate Hall algebra, twisted Hall algebra of $A$ and those of $C_1(\mathscr{P})$, respectively.

Homology of path complexes and hypergraphs

The path complex and its homology were defined in previous papers of the authors. The notion of a path complex is a natural discrete generalization of the notion of a simplicial complex. The theory of path complexes contains homotopy invariant homology theory of digraphs and (nondirected) graphs.In the paper we study the homology theory of path complexes. In particular, we describe functorial properties of paths complexes, introduce the notion of homotopy for path complexes and prove the homotopy invariance of path homology groups. We prove also several theorems that are similar to the results of classical homology theory of simplicial complexes. Then we apply this approach to construct homology theories on various categories of hypergraphs. We describe basic properties of these homology theories and relations between them. As a particular case, these results give new homology theories on the category of simplicial complexes.

Synthesis, characterization and antimicrobial studies of some metal complexes with mixed ligands derived from Mannich bases and diamine ligands

The present study deals with the structure and antimicrobial properties of a new series complexes of Fe(II), Co(II), Ni(II), Cu(II) and Zn(II) ions with mixed ligands involved Mannich ligand (L) and diamine ligand (L’).L=Mannich ligands involved L1, L2, L3 namely:L1 = N-[1-Morpholino-(3-methoxy,4-hydroxy)benzyl]acetamide (MBA)L2 = N-[1-Morpholino-(3-methoxy,4-hydroxy)benzyl]Benzamide (MBB)L3 = N-[1-Morpholino-(3-methoxy,4-hydroxy)benzyl]Urea (MBU)L’ Ligand is a 1,10-phenanthroline.These complexes were prepared from the direct reaction of the metal (II) chloride, mannich bases (MBA, MBB, MBU) and diamine ligand namely with mole ration (2:1:1) of L:M:L’ categories of complexes were synthesis is mononuclear complexes of formula:[M(L)2(L’)].nH2O whereM = Fe(II), Co(II), Ni(II), Cu(II), Zn(II).L = Mannich base (MBA, MBB, MBU).L’ = 1,10-phenanthroline.The structure of each complex was characterized by spectroscopic methods (IR, UV-Visible), molar conductivity, elemental analysis (C.H.N) and atomic absorption techniques as well as magnetic data. The completion of the reaction checked by using TLC. The mannich bases (L) and diamine ligands coordinated to the metal ion as bidentated ligands through the oxygen atom of the carbonyl group of amide, nitrogen atom of morpholine and two nitrogen atoms of diamine ligand. The following geometrical with all metal ions showed octahedral geometry. Antibacterial activity of the ligand and its complexes was tested against some select bacterial.

How Far Can One Push the Noble Gases Towards Bonding?: A Personal Account.

Noble gases (Ngs) are the least reactive elements in the periodic table towards chemical bond formation when compared with other elements because of their completely filled valence electronic configuration. Very often, extreme conditions like low temperatures, high pressures and very reactive reagents are required for them to form meaningful chemical bonds with other elements. In this personal account, we summarize our works to date on Ng complexes where we attempted to theoretically predict viable Ng complexes having strong bonding to synthesize them under close to ambient conditions. Our works cover three different types of Ng complexes, viz., non-insertion of NgXY type, insertion of XNgY type and Ng encapsulated cage complexes where X and Y can represent any atom or group of atoms. While the first category of Ng complexes can be thermochemically stable at a certain temperature depending on the strength of the Ng-X bond, the latter two categories are kinetically stable, and therefore, their viability and the corresponding conditions depend on the size of the activation barrier associated with the release of Ng atom(s). Our major focus was devoted to understand the bonding situation in these complexes by employing the available state-of-the-art theoretic tools like natural bond orbital, electron density, and energy decomposition analyses in combination with the natural orbital for chemical valence theory. Intriguingly, these three types of complexes represent three different types of bonding scenarios. In NgXY, the strength of the donor-acceptor Ng→XY interaction depends on the polarizing power of binding the X center to draw the rather rigid electron density of Ng towards itself, and sometimes involvement of such orbitals becomes large enough, particularly for heavier Ng elements, to consider them as covalent bonds. On the other hand, in most of the XNgY cases, Ng forms an electron-shared covalent bond with X while interacting electrostatically with Y representing itself as [XNg]+Y−. Nevertheless, in some of the rare cases like NCNgNSi, both the C-Ng and Ng-N bonds can be represented as electron-shared covalent bonds. On the other hand, a cage host is an excellent moiety to examine the limits that can be pushed to attain bonding between two Ng atoms (even for He) at high pressure. The confinement effect by a small cage-like B12N12 can even induce some covalent interaction within two He atoms in the He2@B12N12 complex.

Sequential, Structural and Functional Properties of Protein Complexes Are Defined by How Folding and Binding Intertwine

Intrinsically disordered proteins (IDPs) fulfill critical biological roles without having the potential to fold on their own. While lacking inherent structure, the majority of IDPs do reach a folded state via interaction with a protein partner, presenting a deep entanglement of the folding and binding processes. Protein disorder has been recognized as a major determinant in several properties of proteins, such as sequence, adopted structure upon binding and function. However, the way the binding process is reflected in these features in general lacks a detailed description. Here, we defined three categories of protein complexes depending on the unbound structural state of the interactors and analyzed them in detail. We found that strikingly, the properties of interactors in terms of sequence and adopted structure are defined not only by the intrinsic structural state of the protein itself but also to a comparable extent by the structural state of the binding partner. The three different types of interactions are also regulated through divergent molecular tactics of post-translational modifications. This not only widens the range of biologically relevant sequence and structure spaces defined by ordered proteins but also presents distinct molecular mechanisms compatible with specific biological processes, separately for each interaction type. The distinct attributes of different binding modes identified in this study can help to understand how various types of interactions serve as building blocks for the assembly of tightly regulated and highly intertwined regulatory networks.

Luminescent, Redox-Active Dithiolatobis(imine)platinum(II) Divergent Complexes with Exchangeable Imine Ligands: An Experimental/Computational Study Versus Their Diiminedithiolatoplatinum(II) Convergent Congeners

This article provides a third manifestation of a new tradition by which the editors of Comments on Inorganic Chemistry wish to lead by example, whereby we start publishing original research content that, nonetheless, preserves the journal’s identity as a niche for “critical discussion” of contemporary literature in inorganic chemistry. (For the first and second manifestations, see: (1) Otten, B. M.; Melancon, K. M.; Omary, M. A. “All that Glitters is Not Gold: A Computational Study of Covalent vs Metallophilic Bonding in Bimetallic Complexes of d10 Metal Centers: A Tribute to Al Cotton on the 10th Anniversary of His Passing,” Comments Inorg. Chem. 2018, 38, 1–35; (2) Yaseen, W. K.; Sanders, S. F.; Almotawa, R. M.; Otten, B. M.; Bhat, S.; Alamo, D. C.; Marpu, S. B.; Golden, T. D.; Omary, M. A. “Are Metal Complexes ‘Organic’, ‘Inorganic’, ‘Organometallic’, or ‘Metal-Organic’ Materials? A Case Study for the Use of Trinuclear Coinage Metal Complexes as ‘Metal-Organic Coatings’ for Corrosion Suppression on Aluminum Substrates,” Comments Inorg. Chem. 2019, 39, 1–26.) Herein, we contrast the electronic structure of two categories of Pt(II) complexes with mixed imine/thiolato ligands: a new class of [Pt(N^N)2(S^S)] bis(κ1-diimine)dithiolatoplatinum(II) divergent complexes—whereby only one N atom from the “back-to-back” diimine ligand actually coordinates to a Pt(II) center in a non-bridging monodentate manner—vis-à-vis the hitherto well-studied [Pt(N^N)(S^S)] (κ2-diimine)dithiolatoplatinum(II) convergent congeners—whereby both the diimine and dithiolate coordinate as κ2-chelating bidentate. Thus, in pursuit of using luminescent building blocks to generate light-harvesting supramolecular coordination compounds, we report the synthesis, characterization, and reactivity of Pt(pyz)2(mnt), 1, in high yield (pyz = pyrazine, mnt = maleonitriledithiolate). The complex exhibits solvent-dependent exchange of the pyrazine ligands, which can be utilized in the formation of larger complexes containing platinum dithiolate moieties. As proof of concept, 1 has been converted into the more inert Pt(4,4ʹ-bpy)2(mnt), 2, and Pt(4-ap)2(mnt), 3, (4-ap = 4-aminopyridine) complexes. These complexes exhibit redox properties, are strong absorbers of ultraviolet and visible light, and exhibit bright-luminescence at 77 K. Single-crystal X-ray diffraction analysis for 1 and 3 confirms the monotopic coordination of the ligands with intramolecular Pt-S and Pt-N bond lengths being comparable to other complexes of type (κ2-diimine)(dithiolate)Pt(II), whereas significant torsion is exhibited by the two heterocyclic rings due to the lack of tethering to one another. Solvent-dependent stability is uncovered for 1 crystals, whereas the crystal structure of 3 reveals an interesting supramolecular quadrangle resulting from hydrogen bonding between the amine groups of two complexes and two interstitial water molecules. A commentary is presented to contrast the electronic structure of the divergent complexes herein with that of a diimine-dithiolate analogue. Experimentally, the luminescence is believed to be sensitized in the new class of divergent complexes, given that their lack of conjugation of two aromatic rings renders them less-efficient π-acceptors compared to analogous diimines such as 2,2ʹ-bipyridine (2,2ʹ-bpy), hence blue-shifting the absorption toward the blue/near-UV and assisting in keeping the emission well within the visible region, whereby energy gap law considerations would suppress quenching effects in the red/near-infrared regions, especially under experimental conditions conducive for phosphorescence and aggregation effects in the solid state and higher-concentration fluid and/or frozen solutions. Computational studies for monomeric models of the three divergent complexes plus the diimine-dithiolate congener, Pt(2,2ʹ-bpy)(mnt), attain reasonable agreement with experimental structural, spectroscopic, and redox properties and provide excellent insights for the comparison between the two categories of complexes upon which we focus the commentary section. The computed photophysical properties reveal phosphorescence due to higher-lying triplet states, as the T1 is found to luminesce in the near-IR region and entail a ligand-field (dd) transition origin, whereas higher-lying states are shown to be in the visible region, close to experimental phosphorescence energies, and are consistent with the expected charge transfer transition to imine/diimine lowest-unoccupied molecular orbitals (LUMOs) from admixed dithiolate/platinum highest-occupied molecular orbitals (HOMOs). The T1 state is likely the culprit for the vanishing emission intensity at ambient temperature for both classes of complexes. We also find that both the T1 and D1 states for the neutral exciton and radical polaron (anion or cation) species, respectively, are severely distorted in 1–3 vs Pt(2,2ʹ-bpy)(mnt) models. Near-perfect orthogonality of the two heterocyclic rings can be attained for such excited and redox models of Pt(κ1-imine)2(dithiolate), whereas this distortion is hindered in Pt(κ2-diimine)(dithiolate) models due to the steric constraint in their CCNNPt metallacycle.

Finiteness Criteria in Quasi-resolving Subcategories

Quasi-resolving subcategory, as a generalization of resolving subcategory, was introduced in Zhu (J Algebra 414:6–40, 2014). Let $${\mathcal {A}}$$ be an abelian category, $${\mathcal {X}}$$ a quasi-resolving subcategory of $${\mathcal {A}}$$ and $${\mathcal {H}}$$ an Ext-injective cogenerator for $${\mathcal {X}}$$ . We study the subcategory consisting of all the objects with finite $${\mathcal {X}}$$ -resolution dimension. Furthermore, we investigate the objects with approximations by objects which are either with finite $${\mathcal {H}}$$ -resolution dimension or else in $${\mathcal {X}}$$ . As applications, we give the finiteness criteria of the homological dimensions in Gorenstein categories of modules and complexes.

Spanier–Whitehead K-duality for C∗-algebras

Classical Spanier–Whitehead duality was introduced for the stable homotopy category of finite CW complexes. Here we provide a comprehensive treatment of a noncommutative version, termed Spanier–Whitehead [Formula: see text]-duality, which is defined on the category of [Formula: see text]-algebras whose [Formula: see text]-theory is finitely generated and that satisfy the UCT, with morphisms the [Formula: see text]-groups. We explore what happens when these assumptions are relaxed in various ways. In particular, we consider the relationship between Paschke duality and Spanier–Whitehead [Formula: see text]-duality.