Monoidal bicategories and extensions of gr-categories
type: Item
instance of: scholarly article
title: Monoidal bicategories and extensions of gr-categories
zbMATH Open document ID: 1068.18007
published in: Homology, Homotopy and Applications
publication date: 2005-04-05T00:00:00Z
full work available at URL: volume5-1.htm
review text: Defining the kernel as a homotopy fiber, the author finds the good way to generalize the Schreier-Breen theory. Extensions of gr-categories (i.e., categorical groups or monoidal categories in which all morphisms are iso) are defined and classified. The main result constructs a biequivlence between the 2-category \(\text{Ext}(K,G)^{\text{op}}\) and the bicategory \(\text{Bimon}(K,\text{Bieq}(G))\) of monoidal bicategory homomorphisms between \(K\) and \(\text{Bieq}(G)\), the monoidal bicategory of biequivalences of \(G\) with itself. One has a fundamental work of explicitation, particularly for coherence constraints in monoidal 2-categories.
reviewed by: Georges Hoff
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 18G15
Mathematics Subject Classification ID: 18G50
zbMATH DE Number: 2153129
zbMATH Keywords: gr-category
zbMATH Keywords: categorical group
zbMATH Keywords: extension
zbMATH Keywords: homotopy kernel
MaRDI profile type: Publication
DOI: 10.4310/HHA.2003.V5.N1.A19
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description: scientific article; zbMATH DE number 2153129