Function spaces and classifying spaces of algebras over a prop

Yalin, Sinan

doi:10.2140/agt.2016.16.2715

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Function spaces and classifying spaces of algebras over a prop

Sinan Yalin

Algebraic & Geometric Topology 16 (2016) 2715–2749

DOI: 10.2140/agt.2016.16.2715

Abstract

The goal of this paper is to prove that the classifying spaces of categories of algebras governed by a prop can be determined by using function spaces on the category of props. We first consider a function space of props to define the moduli space of algebra structures over this prop on an object of the base category. Then we mainly prove that this moduli space is the homotopy fiber of a forgetful map of classifying spaces, generalizing to the prop setting a theorem of Rezk.

The crux of our proof lies in the construction of certain universal diagrams in categories of algebras over a prop. We introduce a general method to carry out such constructions in a functorial way.

Keywords

props, classifying spaces, moduli spaces, bialgebras category, homotopical algebra, homotopy invariance

Mathematical Subject Classification 2010

Primary: 18D10, 18D50, 18G55, 55U10

References

Publication

Received: 5 February 2015

Revised: 26 February 2016

Accepted: 6 March 2016

Published: 7 November 2016

Authors

Sinan Yalin
Department of Mathematical Sciences University of Copenhagen Universitetsparken 5 2100 Copenhagen Denmark

Volume 16, issue 5 (2016)