Zappa-Sz\'ep products for partial actions of groupoids on Left Cancellative Small Categories
Eduard Ortega, Enrique Pardo

TL;DR
This paper explores the structure of groupoid actions on left cancellative small categories, focusing on their Zappa-Szép product constructions, properties of the associated tight groupoids, and conditions for amenability.
Contribution
It introduces a framework connecting left cancellative small categories with Zappa-Szép products and characterizes properties of the resulting tight groupoids, including amenability.
Findings
Certain categories can be represented as Zappa-Szép products.
Characterization of when the tight groupoid is Hausdorff, effective, and minimal.
Conditions under which the tight groupoid is amenable.
Abstract
We study groupoid actions on left cancellative small categories and their associated Zappa-Sz\'ep products. We show that certain left cancellative small categories with nice length functions can be seen as Zappa-Sz\'ep products. We compute the associated tight groupoids, characterizing important properties of them, like being Hausdorff, effective and minimal. Finally, we determine amenability of the tight groupoid under mild, reasonable hypotheses.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topology and Set Theory · Advanced Operator Algebra Research
