Centre for Mathematics, University of Coimbra

<Reference List>
Type:	Preprint
National /International:	International
Title:	KZ-monadic categories and their logic
Publication Date:	2016-06-21
Authors:	- Jirí Adámek - Lurdes Sousa
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 Top₀) it is also complete for every set H of squares.
Institution:	DMUC 16-32
Online version:	http://www.mat.uc.pt/preprints/eng_2016.htm
Download:	Not available