Conditionally Reversible Computations and Weak Universality in Category Theory

Abstract

The main attention is directed to the notion of weak universality in category theory. While the definitions based on the ordinary universal constructions usually hold up to isomorphisms, that is, unconditionally reversible arrows, weakly universal constructions may be seen “positively” as defined up to conditionally reversible arrows. It is shown that weak universality is closely related to intensional equality, typically considered in categories used in computer science. As a possible application of weakly universal categorical constructions we suggest the notion of a conditionally reversible computation in the theory of computations. Bibliography: 6 titles.