2019/02/26 by Laura Jakobsson, Jakobsson, Laura · 1 citation
Computer Science · Mathematics · Pharmacology, Toxicology and Pharmaceutics · #05E40 #Algebraic Topology (math.AT) #Alkaloids: synthesis and pharmacology #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1902.09873
openalex publication_date 2019/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cellular resolutions is a well studied topic on the level of single resolutions and certain specific families of cellular resolutions. One question coming out of the work on families is to understand the structure of cellular resolutions more generally. We give a starting point to understanding higher level structures by defining the category of cellular resolutions. In this paper we study the properties of this category. The main results are in lifting homotopy colimits from topology and Morse theory on cellular resolution being compatible with the category.