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arXiv · 2107.06202

Morse theory for loop-free categories

Michał Lipiński·David Mosquera-Lois·Mateusz Przybylski
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Abstract

We extend discrete Morse-Bott theory to the setting of loop-free (or acyclic) categories. First of all, we state a homological version of Quillen's Theorem A in this context and introduce the notion of cellular categories. Second, we present a notion of vector field for loop-free categories. Third, we prove a homological collapsing theorem in the absence of critical objects in order to obtain the Morse inequalities. Examples are provided through the exposition. This answers partially a question by T. John: whether there is a Morse theory for loop-free (or acyclic) categories? [14].

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BibTeXRIS

Michał Lipiński, David Mosquera-Lois, Mateusz Przybylski. 2021-07-13. Morse theory for loop-free categories. https://arxiv.org/abs/2107.06202

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