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.
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