منابع مشابه
Computing left Kan extensions
We describe a new extension of the Todd–Coxeter algorithm adapted to computing left Kan extensions. The algorithm is a much simplified version of that introduced by Carmody and Walters (Category Theory, Proceedings of the International Conference Held in Como, Italy, 22–28 July 1990. Springer) in 1991. The simplification allows us to give a straightforward proof of its correctness and terminati...
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An existing procedure to compute left Kan extensions over the ground category Set also computes left Kan extensions over the ground categories Cat, 2-Cat, n-Cat for any n and indeed !-Cat. Therefore extension data struc-tured in this manner already can make use of the left Kan extension notion of a best possible approximation. Examples include systems of labeled transition systems and certain h...
متن کاملKan Extensions of Institutions
Institutions were introduced by Goguen and Burstall 8, 9, 10, 11] to formally capture the notion of logical system. Interpreting institutions as functors, and morphisms and representations of institutions as natural transformations, we give elegant proofs for the completeness of the categories of institutions with morphisms and representations, respectively, show that the duality between morphi...
متن کاملPostulated colimits and left exactness of Kan-extensions
If A is a small category and E a Grothendieck topos, the Kan extension LanF of a flat functor F : A → E along any functor A → D preserves whatever finite limits may exist in D; this is a well known fundamental result in topos theory. We shall present a metamathematical argument to derive out of this some other left exactness results, for Kan extensions with values in a (possibly large) site E. ...
متن کاملKan Extensions of Institutions
Institutions were introduced by Goguen and Burstall [GB84, GB85, GB86, GB92] to formally capture the notion of logical system. Interpreting institutions as functors, and morphisms and representations of institutions as natural transformations, we give elegant proofs for the completeness of the categories of institutions with morphisms and representations, respectively, show that the duality bet...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2003
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(02)00102-5