REVIEW 2 cited by
Proto-exact and parabelian categories
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
Proto-exact and parabelian categories serve as non-additive analogues of exact and quasi-abelian categories, respectively. They give rise to algebraic K-theory and Hall algebras similarly to the additive setting. We show that every parabelian category admits a canonical proto-exact structure and we study several classes of parabelian categories, including categories of normed and Euclidean vector spaces, pointed closure spaces and pointed matroids, Hermitian vector bundles over rings of integers. We also examine finitary algebraic categories arising in Arakelov geometry and provide a criterion for determining when such a category is parabelian. In particular, we prove that the categories of pointed convex spaces and absolutely convex spaces are parabelian.
Forward citations
Cited by 2 Pith papers
-
Quotients of mosaics and related hyperstructures
Effective congruences on mosaics are exactly regular sub-mosaics of M×M satisfying two closure conditions, and the category of mosaics is parabelian.
-
Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves
The authors prove that pointed matroids over perfect idylls form a combinatorial proto-exact category with duality and exact direct sum, and that tropical toric reflexive sheaves (modular ones in particular) are proto...
Discussion (0). Continue with ORCID to comment.