Geodesic
Conditionally reversible computations and weak universality in category theory
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Tome 421 (2014), pp. 19-32 
S. N. Baranov; S. V. Soloviev. Conditionally reversible computations and weak universality in category theory. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Tome 421 (2014), pp. 19-32. http://geodesic.mathdoc.fr/item/ZNSL_2014_421_a1/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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, unconditionnally reversible arrows, weakly universal constructions may be seen “positively” as defined up to conditionnally reversible arrows. It is shown that weak universality is closely connected with intensional equality, typically considered in categories used in computer science. As a possible application of weakly universal categorical constructions we suggest the notion of conditionnally reversible computation in the theory of computations.

[1] A. Asperti, G. Longo, Categories, types, and structures – an introduction to category theory for the working computer scientist, Found. Comput. Ser., MIT Press, 1991 | MR | Zbl

[2] D. Chemouil, “Isomorphisms of simple inductive types through extensional rewriting”, Math. Structures Computer Sci., 15:5 (2005), 875–917 | DOI | MR

[3] Z. Luo, Computation and reasoning. A type theory for computer science, International Series of Monographs on Computer Science, 11, Oxford Science Publications, Clarendon Press, Oxford, 1994 | MR | Zbl

[4] S. Mac Lane, Categories for the working mathematician, Graduate Texts in Mathematics, 5, 2nd edition, Springer-Verlag, 1998 | MR

[5] P. Martin-Löf, Intuitionistic type theory, Notes by G. Sambin of a series of lectures given in Padua, June 1980, Bibliopolis, 1984 | MR | Zbl

[6] M. Saeedi, I. L. Markov, Syntheisis and optimization of reversible circuits – A Survey, 12 Oct. 2011, arXiv: 1110.2574v1[cs.ET]