Y. Lafont. Logiques, Categories & Machines. Th`ese de Doctorat, Universit'e Paris VII, 1988. Home/Search Document Not in Database Summary Related Articles Check |
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Notes on Sconing and Relators - Mitchell, Scedrov (1993) (28 citations) (Correct)
.... mathematical tool used in this work is the category theoretic method of sconing described in Freyd and Scedrov [FrS90] and also called glueing or Freyd covers, see Lambek and Scott [LS86] To our knowledge, the first application of this method to type disciplines is given in Appendix C of Lafont [Laf88]. In the case of simple types, this method corresponds closely to so called logical relations, described for instance in Plotkin [Plo80] Statman [Sta85] and Mitchell [Mit90] This correspondence is examined in detail. In the case of polymorphic types, a central role is played by relators, i.e. ....
....category C 0 with equalizers and the functor j Delta j: C Gamma Set replaced by any functor F: C Gamma C 0 that preserves products up to isomorphism. This generalization takes us from the specific comma category C = Set # j Delta j) to a more general case of the form (C 0 # F) see [Laf88, MaR92]. Proposition 4.2 Let C and C 0 be cartesian closed categories and assume C 0 has equalizers. Let F: C Gamma C 0 be a functor that preserves finite products up to isomorphism. Then the comma category (C 0 # F) is a cartesian closed category and the canonical functor (C 0 # F) Gamma ....
Y. Lafont. Logiques, Categories & Machines. Th`ese de Doctorat, Universit'e Paris VII, 1988.
A Characterization Of Lambda Definability In Categorical Models .. - Alimohamed (1995) (11 citations) (Correct)
....models [Pit87, See87] of the Girard Reynolds polymorphic lambda calculus. To keep this paper self contained, the definitions of iml category and iml representation are given in Section 2. The starting point of this work is the category theoretic technique of sconing or glueing described in [FrS90, Laf88, MaR91, MSd93]. A glueing functor Gamma : A Gamma D is any functor that preserves finite products up to isomorphism. If A is any cartesian closed category (or ccc) and D is any ccc with pullbacks, then a glueing functor Gamma gives rise to a new ccc (D# Gamma) and a canonical forgetful functor Sigma : D# ....
.... A) S; B) is the pair (M;A ) B) where M = Phi f 2 Gamma(A ) B) fi fi Gamma(ffl A;B ) j(f; a) 2 S for all a 2 R Psi : It is well known that the category S in the preceeding discussion may be replaced by any ccc D with pullbacks to yield a subscone (D # Gamma) for details consult [Laf88, MaR91, MSd93]) However for the purposes of this paper, it will be sufficient to consider D to be either S or a Kripke presheaf category S W ffi . 1.2. Sconing with Henkin models into sets. Fix a set S of ground types and let A = Omega fA oe g; fApp oe; g; fP roj oe; i g; ff be a Henkin model of ....
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Y. Lafont. Logiques, Categories & Machines. Th`ese de Doctorat, Universit'e Paris VII, 1988.
Glueing Algebraic Structures on a 2-Category - Hasegawa (2000) (Correct)
....structure, for which q is strict. 4 Full Completeness via Glueing We conclude this note by sketching how a glueing construction can be used for relating algebraic structures on Cat (and the corresponding type theories) further examples are found in [2, 3] and papers cited there, in particular [7]. Let SMCat be the category of small symmetric monoidal categories and strict symmetric monoidal functors, and SMCCat be that of small symmetric monoidal closed categories and strict symmetric monoidal closed functors. The forgetful functor from SMCCat to SMCat has a left adjoint F : SMCat ....
Lafont, Y. (1988) Logiques, Cat'egories et Machines, Th`ese de Doctorat, Universit 'e Paris VII.
Normalization and the Yoneda Embedding - Cubric, Dybier, Scott (Correct)
....Moreover, they focussed on algebraic aspects and used the fact that syntax modulo conversion is a free model and hence has a unique homomorphic interpretation into any other model. They also related Martin Lof s construction to the glueing construction from category theory, especially as used by (Lafont 1988). In (Martin Lof 1975a; Martin Lof 1975b) he introduced the technique for normalization in typed combinatory logic and weak calculus. The same general technique was 23 used to construct a normalization algorithm for simply typed fij calculus by (Berger and Schwichtenberg 1991) They inverted ....
Y. Lafont. Logiques, cat'egories et machines. Th`ese de doctorat, Universit'e Paris VII, 1988.
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