KZ-monadic categories and their logic

<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <title> KZ-monadic categories and their logic </title> <link REL="stylesheet" TYPE="text/css" href="../../../tac.css"> </head> <body> <h1> KZ-monadic categories and their logic </h1> <h2> Jiri Adamek and Lurdes Sousa </h2> <p> 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. </p> <p> Keywords: order-enriched category, Kan-injectivity, KZ-monad, Kan-injectivity logic, locally ranked category </p> <p> 2010 MSC: 18C20, 18B35, 18D20, 54B30, 06B35,06D22, 18A15 </p> <p><i>Theory and Applications of Categories,</i> <font face="times new roman"> Vol. 32, 2017, No. 10, pp 338-379.</font> </p><p> Published 2017-02-27. </p><p> <a href="http://www.tac.mta.ca/tac/volumes/32/10/32-10.pdf"> http://www.tac.mta.ca/tac/volumes/32/10/32-10.pdf</a><br> </p> <a href ="../../../index.html"> TAC Home </a> </body></html>

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KZ-monadic categories and their logic