English

Categories of Dimension Zero

Representation Theory 2019-04-16 v2

Abstract

If D is a category and k is a commutative ring, the functors from D to k-Mod can be thought of as representations of D. By definition, D is dimension zero over k if its finitely generated representations have finite length. We characterize categories of dimension zero in terms of the existence of a "homological modulus" (Definition 1.4) which is combinatorial and linear-algebraic in nature.

Keywords

Cite

@article{arxiv.1508.04107,
  title  = {Categories of Dimension Zero},
  author = {John D. Wiltshire-Gordon},
  journal= {arXiv preprint arXiv:1508.04107},
  year   = {2019}
}

Comments

15 pages

R2 v1 2026-06-22T10:35:28.593Z