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Title: KZ-monadic categories and their logic
Authors: Adámek, Jiří 
Sousa, Lurdes 
Issue Date: 2017
Publisher: Theory and Applications of Categories
Project: info:eu-repo/grantAgreement/FCT/5876/147205/PT 
Serial title, monograph or event: Theory and Applications of Categories
Volume: 32
Abstract: 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.
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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