Garside and locally Garside categories
Fran\c{c}ois Digne (LAMFA), Jean Michel (IMJ)
TL;DR
This paper introduces axioms for Garside and locally Garside categories, providing a framework that applies to Coxeter and Artin groups as well as Deligne-Lusztig varieties, enhancing understanding of their algebraic structures.
Contribution
It establishes a new axiomatic framework for Garside and locally Garside categories, extending their applicability to important algebraic and geometric structures.
Findings
Defined axioms for Garside categories
Extended Garside concepts to locally Garside categories
Applied framework to Coxeter, Artin groups, and Deligne-Lusztig varieties
Abstract
We define and give axioms for Garside and locally Garside categories. We give an application to Coxeter and Artin groups and Deligne-Lusztig varieties.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Advanced Topics in Algebra