Translator Disclaimer
2016 Function spaces and classifying spaces of algebras over a prop
Sinan Yalin
Algebr. Geom. Topol. 16(5): 2715-2749 (2016). DOI: 10.2140/agt.2016.16.2715


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.


Download Citation

Sinan Yalin. "Function spaces and classifying spaces of algebras over a prop." Algebr. Geom. Topol. 16 (5) 2715 - 2749, 2016.


Received: 5 February 2015; Revised: 26 February 2016; Accepted: 6 March 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1352.18004
MathSciNet: MR3572346
Digital Object Identifier: 10.2140/agt.2016.16.2715

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

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 5 • 2016
Back to Top