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Zap. Nauchn. Sem. POMI, 2014, Volume 421, Pages 19–32 (Mi znsl5746)  

Conditionally reversible computations and weak universality in category theory

S. N. Baranova, S. V. Solovievb

a SPIIRAS, Russian Academy of Sciences, St. Petersburg, Russia
b IRIT, University of Toulouse, France

Abstract: 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.

Key words and phrases: weak universality in categories, extensional and intensional equality, conditionnally reversible computations.

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English version:
Journal of Mathematical Sciences (New York), 2014, 200:6, 654–661

UDC: 512.58+510.64+510.51
Received: 12.11.2013
Language:

Citation: S. N. Baranov, S. V. Soloviev, “Conditionally reversible computations and weak universality in category theory”, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Zap. Nauchn. Sem. POMI, 421, POMI, St. Petersburg, 2014, 19–32; J. Math. Sci. (N. Y.), 200:6 (2014), 654–661

Citation in format AMSBIB
\Bibitem{BarSol14}
\by S.~N.~Baranov, S.~V.~Soloviev
\paper Conditionally reversible computations and weak universality in category theory
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXIII
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 421
\pages 19--32
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5746}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 200
\issue 6
\pages 654--661
\crossref{https://doi.org/10.1007/s10958-014-1955-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84940264334}


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