Cohomological results in monoid and category theory via classifying spaces
type: Item
instance of: scholarly article
title: Cohomological results in monoid and category theory via classifying spaces
zbMATH Open document ID: 0837.18006
DOI: 10.1016/0022-4049(94)00056-O
author: Marc Nunes
published in: Journal of Pure and Applied Algebra
publication date: 1996-05-13T00:00:00Z
review text: This work considers topological, homotopical and homological methodology in the study of monoids via the classifying space functor \(|\;|: {\mathcal C}at\to{\mathcal T}op\). An important adjunction \({\mathcal C}at\downarrow C\rightleftarrows{\mathcal C}at^{C^{op}}\) is described and used. Conditions are studied for the classifying space of a monoid to be equivalent to a finite-dimensional CW-complex. Spectral sequences associated to some functors give results (e.g., for the computation of the Euler characteristic of \(|C|\)). Informations are given to know when a surmorphism is a (co)homological equivalence.
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 18G40
Mathematics Subject Classification ID: 18A20
zbMATH DE Number: 802561
zbMATH Keywords: cohomology
zbMATH Keywords: classifying space of monoid
zbMATH Keywords: spectral sequences
zbMATH Keywords: monoids
zbMATH Keywords: classifying space functor
zbMATH Keywords: CW-complex
zbMATH Keywords: Euler characteristic
reviewed by: Georges Hoff
MaRDI profile type: Publication
cites work: Q3708977
cites work: Q4132170
cites work: Q4693151
cites work: Q3582378
cites work: Decomposition techniques for finite semigroups, using categories. II
cites work: Q5522742
cites work: Categories as algebra: An essential ingredient in the theory of monoids
cites work: Higher algebraic K-theory: I
cites work: Q3996901
cites work: Q5530411
description: scientific article; zbMATH DE number 802561