Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Function spaces and classifying spaces of algebras over a prop   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.

21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat