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Coherence and valid isomorphism in closed categories applications of proof theory to category theory in a computer sclentist perspective

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Category Theory and Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 389))

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References

  • Asperti A., Longo G. [1989] Applied category theory: an introduction to categories, types and structures for the working computer scientist, M.I.T. Press, to appear.

    Google Scholar 

  • Bruce K., Longo G. [1985] “Provable isomorphisms and domain equations in models of typed languages,” (Preliminary version) 1985 A.C.M. Symposium on Theory of Computing (STOC 85), Providence (R.I.), May, (263–272).

    Google Scholar 

  • Dezani M. [1976] “Characterization of normal forms possessing an inverse in the λβη-calculus,” Theor. Comp. Sci., 2 (323–337).

    Google Scholar 

  • Kelly G.M., Mac Lane S.,[1971] “Coherence in closed categories”, J. Pure Appl. Algebra, no 1, (97–140); erratum, ibid. no 2, 219.

    Google Scholar 

  • Lambek J., [1968] “Deductive systems and categories I, Syntactic calculus and residuated categories”, Math. Systems Theory 2, (287–318).

    Google Scholar 

  • Lambek J., [1969] “Deductive systems and categories II, Standard constructions and closed categories”, Lecture Notes in Math., Vol. 86, Springer r-Verlag, Berlin (76–122).

    Google Scholar 

  • Mac Lane S. [1963] “Natural associativity and commutativity”, Rice University Studies 49 (28–46).

    Google Scholar 

  • Mac Lane S. [1976] “Topology and logic as a source of algebra” (retiring Presidential address), Bull Amer. Math. Soc. 82, n o, 1, (1–40).

    Google Scholar 

  • Minc G.E. [1972] “A cut elimination theorem for relevant logics” (Russian English summary), Investigations in constructive mathematics and mathematical logic V. Zap. Naucn Sem. Leningrad Otdel mat. Inst. Steklov (LOMI) 32, (90–97); 156.

    Google Scholar 

  • Minc G.E., [1977] “Closed categories and the theory of proofs (Russian, English Summary)”, Zap Naucn. Sem. Leningrad Otdel Mat. Inst. Steklov (LOMI) 68, (83–114); 145. (Trans circulated as preprint).

    Google Scholar 

  • Minc G.E. [197?] “A simple proof of the coherence theorem for cartesian closed categories” Bibliopolis (to appear in translation from russian).

    Google Scholar 

  • Minc G.E. [197?] “Proof theory and category theory” Bibliopolis (to appear in translation from russian).

    Google Scholar 

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David H. Pitt David E. Rydeheard Peter Dybjer Andrew M. Pitts Axel Poigné

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© 1989 Springer-Verlag Berlin Heidelberg

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Longo, G. (1989). Coherence and valid isomorphism in closed categories applications of proof theory to category theory in a computer sclentist perspective. In: Pitt, D.H., Rydeheard, D.E., Dybjer, P., Pitts, A.M., Poigné, A. (eds) Category Theory and Computer Science. Lecture Notes in Computer Science, vol 389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018341

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  • DOI: https://doi.org/10.1007/BFb0018341

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  • Print ISBN: 978-3-540-51662-0

  • Online ISBN: 978-3-540-46740-3

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