Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On homotopy exponentials in path categories   In the first part of this paper we show that path categories are enriched
over groupoids, in a way that is compatible with a suitable 2-category of path
categories. In the second part we introduce a new notion of homotopy
exponential and homotopy Pi-type for path categories, the strong homotopy
exponential and the strong homotopy Pi-type. We prove some of their basic
properties, along with two important technical propositions. The results in the
second part of this paper are mostly obtained using the groupoid enrichment of
path categories established in the first part.

6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas