منابع مشابه
Free models of T -algebraic theories computed as Kan extensions
One fundamental aspect of Lawvere’s categorical semantics is that every algebraic theory (eg. of monoid, of Lie algebra) induces a free construction (eg. of free monoid, of free Lie algebra) computed as a Kan extension. Unfortunately, the principle fails when one shifts to linear variants of algebraic theories, like Adams and Mac Lane’s PROPs, and similar PROs and PROBs. Here, we introduce the ...
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 کاملComputing 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...
متن کاملLeft Kan Extensions Over !-Cat
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 [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: Ghendtsche Tydinghen
سال: 2017
ISSN: 1783-9033
DOI: 10.21825/gt.v46i2.16932