Geodesic
KZ-monadic categories and their logic
Theory and applications of categories, Tome 32 (2017), pp. 338-379

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Given an order-enriched category, it is known that all its KZ-monadic subcategories can be described by Kan-injectivity with respect to a collection of morphisms. We prove the analogous result for Kan-injectivity with respect to a collection H of commutative squares. A square is called a Kan-injective consequence of H if by adding it to H Kan-injectivity is not changed.We present a sound logic for Kan-injectivity consequences and prove that in ``reasonable" categories (such as $\Pos$ or $\Top_0$) it is also complete for every set H of squares.

Publié le :
Classification : 18C20, 18B35, 18D20, 54B30, 06B35, 06D22, 18A15
Keywords: order-enriched category, Kan-injectivity, KZ-monad, Kan-injectivity logic, locally ranked category 
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     author = {Jiri Adamek and Lurdes Sousa},
     title = {KZ-monadic categories and their logic},
     journal = {Theory and applications of categories},
     pages = {338--379},
     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a9/}
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Jiri Adamek; Lurdes Sousa. KZ-monadic categories and their logic. Theory and applications of categories, Tome 32 (2017), pp. 338-379. http://geodesic.mathdoc.fr/item/TAC_2017_32_a9/