Benabou, J. Fibred categories and the foundations of naive category theory. Journal of Symbolic Logic 50, 1985, 10-37. Home/Search Document Not in Database Summary Related Articles Check |
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A General Semantics for Evaluation Logic - Moggi (1994) (4 citations) (Correct)
....for SFPs. We skip the details. 4 A new semantics of EL T In this section we consider a semantics for the necessity modality of EL T , which is based on di erent assumptions about C, M and T . We brie y recall the necessary background about brations and factorization systems, and refer to [1, 9] and [2, 5] for more details. De nition 4.1 (Fibrations) Given p: C B, we say that f 2 C(Y; X) is p cartesian ( for every g 2 C(Z; X) and h 0 2 B(pZ; pY ) s.t. pg = h 0 ; pf) exists unique h 2 C(Z; Y ) s.t. g = h ; f and h 0 = ph p: C B is a bration (over B) for ....
J. Benabou. Fibred categories and the foundation of naive category theory. Journal of Symbolic Logic, 50, 1985.
A Category-Theoretic Account of Program Modules - Moggi (1994) (19 citations) (Correct)
.... of type expressions from program expressions, we will consider instead an indexed category C with two D category structures, one for the base and one for the bers (see Section 7) 4 The category of modules The 2 category ICat(B) is isomorphic to the 2 category of split B brations (see [Ben85]) Since B brations are functors with codomain B satisfying certain additional properties, the 2 category of B brations is a 2 subcategory of Cat#B and the 2 embedding, mapping a B indexed category C to the corresponding B bration C : GC B, can be viewed as a 2 functor from ICat(B) to ....
J. Benabou. Fibred categories and the foundation of naive category theory. Journal of Symbolic Logic, 50, 1985.
A semantic view of classical proofs. - type-theoretic, categorical, .. - Ong (1996) (Correct)
....over B objects and A 2 B (1) permutation: Delta Gamma Theta (equivalently invertible maps) 2) weakening: Delta Theta Theta A wA Delta (3) contraction: Delta Theta Theta A c A Delta Theta Theta A Theta Theta A. We shall assume the basics of fibred category theory; see e.g. [3] for an introduction. In the following the definition proper is in italics, explanatory notes and commentary in roman. 4 x A : ff A)B :s)x reduces to ff A)B :s by (j) and to x A : fi B :s[fi; x=ff] by (P) Definition 3.2 A category is a split fibration 0 B B B E #p B 1 C ....
J. Benabou. Fibred categories and the foundations of na ive category theory. J. Symb. Logic, pages 10--37, 1985.
Some Fundamental Algebraic Tools for the Semantics of.. - Tarlecki, Burstall.. (1989) (47 citations) (Correct)
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Benabou, J. Fibred categories and the foundations of naive category theory. Journal of Symbolic Logic 50, 1985, 10-37.
Internal Type Theory - Peter Dybjer Department (1996) (4 citations) (Correct)
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J. B'enabou. Fibred categories and the foundation of naive category theory. Journal of Symbolic Logic, 50:10--37, 1985.
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