Quadratic endofunctors of the category of groups
type: Item
instance of: scholarly article
title: Quadratic endofunctors of the category of groups
zbMATH Open document ID: 0923.20042
published in: Advances in Mathematics
publication date: 1999-08-19T00:00:00Z
review text: Quadratic and more generally polynomial endofunctors have been studied in the literature for additive categories, in particular for the category of abelian groups [\textit{S. Eilenberg} and \textit{S. MacLane}, Ann. Math., II. Ser. 60, 49-139 (1954; Zbl 0055.41704)] and for categories of vector spaces over suitable fields. Polynomial endofunctors of the category of topological spaces have been examined by \textit{T. Goodwillie} [K-Theory 4, No. 1, 1-27 (1990; Zbl 0741.57021); ibid. 5, No. 4, 295-332 (1992; Zbl 0776.55008)]. The purpose of the paper under review is to study quadratic endofunctors on the category of groups. A possible motivation is the observation that polynomial endofunctors of the category of groups applied to simplicial groups yield polynomial endofunctors for spaces. The main result of the paper says that the monoidal category of (suitably defined) quadratic endofunctors of the category of groups is equivalent to the monoidal category of square groups, the notion of square group being defined as a diagram of three groups with appropriate properties.
reviewed by: J. Huebschmann
Mathematics Subject Classification ID: 20J15
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 19D10
zbMATH DE Number: 1251312
zbMATH Keywords: quadratic functors
zbMATH Keywords: endofunctors
zbMATH Keywords: categories of groups
zbMATH Keywords: monoidal categories
author: Hans-Joachim Baues
author: Teimuraz Pirashvili
MaRDI profile type: Publication
full work available at URL: aima.1998.1784
OpenAlex ID: W2062775617
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DOI: 10.1006/AIMA.1998.1784
description: scientific article; zbMATH DE number 1251312