Abstract Excision and $\ell^1$-Homology
Abstract
We use the abstract setting of excisive functors in the language of -categories to show that the best approximation to the -homology functor by an excisive functor is trivial. Then we make an effort to explain the used language on a conceptual level for those who do not feel at home with -categories, prove that the singular chain complex functor is indeed excisive in the abstract sense, and show how the latter leads to classical excision statements in the form of Mayer-Vietoris sequences.
Keywords
Cite
@article{arxiv.2203.06120,
title = {Abstract Excision and $\ell^1$-Homology},
author = {Johannes Witzig},
journal= {arXiv preprint arXiv:2203.06120},
year = {2024}
}
Comments
35 pages; v2: revised version, including: comments on related results (Introduction), more explicit handling of "size" (Introduction, Remarks 2.3, 2.4, 2.11), removal of claim about homology from Theorem 1.7, further explanatory material (Outlook 2.24, Section 2.4); to appear in Confluentes Mathematici