Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variable sets over an algebra of lifetimes: a contribution of lattice
  theory to the study of computational topology   A topos theoretic generalisation of the category of sets allows for modelling
spaces which vary according to time intervals. Persistent homology, or more
generally, persistence is a central tool in topological data analysis, which
examines the structure of data through topology. The basic techniques have been
extended in several different directions, permuting the encoding of topological
features by so called barcodes or equivalently persistence diagrams. The set of
points of all such diagrams determines a complete Heyting algebra that can
explain aspects of the relations between persistent bars through the algebraic
properties of its underlying lattice structure. In this paper, we investigate
the topos of sheaves over such algebra, as well as discuss its construction and
potential for a generalised simplicial homology over it. In particular we are
interested in establishing a topos theoretic unifying theory for the various
flavours of persistent homology that have emerged so far, providing a global
perspective over the algebraic foundations of applied and computational
topology.

24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat