Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poset topology and homological invariants of algebras arising in
  algebraic combinatorics   We present a beautiful interplay between combinatorial topology and
homological algebra for a class of monoids that arise naturally in algebraic
combinatorics. We explore several applications of this interplay. For instance,
we provide a new interpretation of the Leray number of a clique complex in
terms of non-commutative algebra.
  R\'esum\'e. Nous pr\'esentons une magnifique interaction entre la topologie
combinatoire et l'alg\`ebre homologique d'une classe de mono\"ides qui figurent
naturellement dans la combinatoire alg\'ebrique. Nous explorons plusieurs
applications de cette interaction. Par exemple, nous introduisons une nouvelle
interpr\'etation du nombre de Leray d'un complexe de clique en termes de la
dimension globale d'une certaine alg\`ebre non commutative.

15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio