Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak $\infty$-categories via terminal coalgebras   Higher categorical structures are often defined by induction on dimension,
which a priori produces only finite-dimensional structures. In this paper we
show how to extend such definitions to infinite dimensions using the theory of
terminal coalgebras, and we apply this method to Trimble's notion of weak
n-category. Trimble's definition makes explicit the relationship between
n-categories and topological spaces; our extended theory produces a definition
of Trimble infinity-category and a fundamental infinity-groupoid construction.
  Furthermore, terminal coalgebras are often constructed as limits of a certain
type. We prove that the theory of Batanin-Leinster weak infinity-categories
arises as just such a limit, justifying our approach to Trimble
infinity-categories. In fact we work at the level of monads for
infinity-categories, rather than infinity-categories themselves; this requires
more sophisticated technology but also provides a more complete theory of the
structures in question.

21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph