Enhanced 2-categories and limits for lax morphisms | Macquarie University ResearchOnline

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Title: Enhanced 2-categories and limits for lax morphisms
Related: Advances in mathematics, Vol. 229, No. 1, (2012), p.294-356
DOI: 10.1016/j.aim.2011.08.014
Publisher: Elsevier
Date: 2012
Author/Creator: Lack, Stephen
Author/Creator: Shulman, Michael
Description: We study limits in 2-categories whose objects are categories with extra structure and whose morphisms are functors preserving the structure only up to a coherent comparison map, which may or may not be required to be invertible. This is done using the framework of 2-monads. In order to characterize the limits which exist in this context, we need to consider also the functors which do strictly preserve the extra structure. We show how such a 2-category of weak morphisms which is "enhanced, by specifying which of these weak morphisms are actually strict, can be thought of as category enriched over a particular base cartesian closed category F. We give a complete characterization, in terms of F-enriched category theory, of the limits which exist in such 2-categories of categories with extra structure.
Description: 63 page(s)
Subject Keyword: 2-Category
Subject Keyword: 2-Monad
Subject Keyword: Category with structure
Subject Keyword: Enriched category
Subject Keyword: Lax morphism
Subject Keyword: Limit
Subject Keyword: Weak morphism
Resource Type: journal article
Organisation: Macquarie University. Dept. of Mathematics

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