R.A.G. Seely (1989) "Linear logic, -autonomous categories and cofree coalgebras." In J. Gray and A. Scedrov (eds.), Categories in Computer Science and Logic, Contemporary Mathematics 92 (Am. Math. Soc.) 371--382. Home/Search Document Details and Download
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Linear Set Theory - Shirahata (1995) (3 citations) (Correct)
....right adjoint of F . Furthermore, such a pair is called an adoint pair. The composition F ffi G of such a pair is an endofunctor from D to D. Comonads are those endofunctors which can be regarded as a composition of an adjoint pair [17] The observation that is just a comonad is due to R. Seely [27]. Indeed, if we limit ourselves to a special case, can be described in a very neat way. In short, given a closed monoidal category C, we pick up the objects which can be duplicated, i.e. the objects A such that there is a morphism f from A to A Omega A. The pairs (A; f) of such objects and ....
R.A.G. Seely. "Linear logic, -autonomous categories and cofree coalgebras." Categories in Computer Science and Logic, American Mathematical Society, Providence, 1989.
The Logic of Linear Functors - Blute, Cockett (2002) Self-citation (Seely) (Correct)
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R.A.G. Seely (1989) "Linear logic, -autonomous categories and cofree coalgebras." In J. Gray and A. Scedrov (eds.), Categories in Computer Science and Logic, Contemporary Mathematics 92 (Am. Math. Soc.) 371--382.
Categories for Computation in Context and Unified Logic.. - Blute, Cockett, Seely (1997) (2 citations) Self-citation (Seely) (Correct)
No context found.
Seely, R.A.G. "Linear logic, -autonomous categories and cofree coalgebras", in J. Gray and A. Scedrov (eds.), Categories in Computer Science and Logic, Contemporary Mathematics 92 (Am. Math. Soc. 1989).
Categories for Computation in Context and Unified Logic - Blute, Cockett, Seely (1997) (2 citations) Self-citation (Seely) (Correct)
No context found.
Seely, R.A.G. "Linear logic, -autonomous categories and cofree coalgebras", in J. Gray and A. Scedrov (eds.), Categories in Computer Science and Logic, Contemporary Mathematics 92 (Am. Math. Soc. 1989).
Fock Space: A Model of Linear Exponential Types - Blute, Panangaden, Seely (1994) (1 citation) Self-citation (Seely) (Correct)
....[B79] To model the additive connectives, one then adds products and coproducts. Finally, to model the exponentials, and so regain the expressive strength of traditional logic, one adds a triple and cotriple, satisfying properties to be outlined below. This program was first outlined by Seely in [Se89]. Linear logic bears strong resemblance to linear algebra (from which it derives its name) but one significant difference is the difficulty in modelling . The category of vector spaces over an arbitrary field is a symmetric monoidal closed category, indeed in some sense the prototypical ....
....Categories We shall begin with a few preliminaries concerning linear logic. We shall not reproduce the formal syntax of linear logic, nor the usual discussion of its intuitive interpretation or utility for this the reader is referred to the standard references, such as [G87] We do recall [Se89] that a categorical semantics for linear logic may be based on Barr s notion of autonomous categories [B79] If only to establish notation, here is the definition. Definition 1 A category C is autonomous if it satisfies the following: 1. C is symmetric monoidal closed; that is, C has a tensor ....
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Seely, R.A.G. "Linear logic, -autonomous categories and cofree coalgebras", in J. Gray and A. Scedrov (eds.), Categories in Computer Science and Logic, Contemporary Mathematics 92 (Am. Math. Soc. 1989).
Natural Deduction and Coherence for Weakly Distributive .. - Blute, Cockett, Seely, .. (1991) (22 citations) Self-citation (Seely) (Correct)
....that weakly distributive categories share with linear logic [G87] In fact, weakly distributive categories correspond precisely to multiplicative linear logic without negation. This is reflected by the fact that adding negation is precisely what is necessary to obtain autonomous categories [CS91, Se89]. The study of weakly distributive categories is part of a program of modularizing linear logic: that is, allowing the buildup of the logic from as few primitives at the start as possible. Introducing negation as an initial primitive in linear logic seems rather inflexible, and certainly masks ....
Seely, R.A.G. "Linear logic, -autonomous categories and cofree coalgebras", in J. Gray and A. Scedrov (eds.), Categories in Computer Science and Logic, Contemporary Mathematics 92 (Am. Math. Soc. 1989).
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