We survey the basics of homological algebra in exact categories in the sense of Quillen. All
diagram lemmas are proved directly from the axioms, notably the five lemma, the 3× 3 …

For each positive integer n we introduce the notion of n-exangulated categories as higher
dimensional analogues of extriangulated categories defined by Nakaoka–Palu. We …

In this paper, we introduce the signed barcode, a new visual representation of the global
structure of the rank invariant of a multi-parameter persistence module or, more generally, of …

We introduce the notion of an exact dg category, which is a simultaneous generalization of
the notions of exact category in the sense of Quillen and of pretriangulated dg category in …

We define a class of invariants, which we call homological invariants, for persistence
modules over a finite poset. Informally, a homological invariant is one that respects some …

A significant part of modern topological data analysis is concerned with the design and study
of algebraic invariants of poset representations—often referred to as persistence modules …

The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

We fill a gap in the literature regarding 'transport of structure'for (n+ 2)-angulated, n-exact, n-
abelian and n-exangulated categories appearing in (classical and higher) homological …

Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of
properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting) …