Transport of structure in higher homological algebra

Abstract

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 algebra. As an application of our main results, we show that a skeleton of one of these kinds of categories inherits the same structure in a canonical way, up to equivalence. In particular, it follows that a skeleton of a weak (n+2)-angulated category is in fact what we call a strong (n+2)-angulated category. When n=1 this clarifies a technical concern with the definition of a cluster category. We also introduce the notion of an n-exangulated functor between n-exangulated categories. This recovers the definition of an (n+2)-angulated functor when the categories concerned are (n+2)-angulated, and the higher analogue of an exact functor when the categories concerned are n-exact.

v3: 24 pages; minor typographical changes; accepted in Journal of Algebra

References in corpus (4)

• On triangulated orbit categories
• Quantum categories, star autonomy, and quantum groupoids
• The Grothendieck group of an n-angulated category
• A note on transport of algebraic structures

Cited by in corpus (17)

• Higher Auslander's formula
• External triangulation of the homotopy category of exact quasi-category
• The category of extensions and a characterisation of $n$-exangulated functors
• The index with respect to a rigid subcategory of a triangulated category
• Recollements of extriangulated categories
• Idempotent completions of $n$-exangulated categories
• A resolution theorem for extriangulated categories with applications to the index
• Localization of extriangulated categories
• Grothendieck groups of $d$-exangulated categories and a modified Caldero-Chapoton map
• Localization of triangulated categories with respect to extension-closed subcategories
• Cluster categories for completed infinity-gons I: Categorifying triangulations
• From frieze patterns to cluster categories
• The category of extensions and idempotent completion
• s-Recollements and its localization
• Semibricks in extriangulated categories
• Ideal approximation in $n$-angulated categories
• Stratifying systems and Jordan-Hölder extriangulated categories