Relating ample and biample topological categories with Boolean restriction and range semigroups

Autor:	Kudryavtseva, Ganna
Rok vydání:	2024
Předmět:	Mathematics - Rings and Algebras Mathematics - Category Theory 22A22 22A30 20M18 18B40 06E15 06E75
Druh dokumentu:	Working Paper
Popis:	We extend the equivalence by Cockett and Garner between restriction monoids and ample categories to the biunary and non-unital setting of Boolean range semigroups which are non-unital one-object versions of range categories. We show that Boolean range semigroups are equivalent to ample topological categories where the range map $r$ is open, and \'etale Boolean range semigroups are equivalent to biample topological categories. These results yield the equivalence between \'etale Boolean range semigroups and Boolean birestriction semigroups and a characterization when a Boolean restriction semigroup admits a compatible cosupport operation. We also recover the equivalence between Boolean birestriction semigroups and biample topological categories by Kudryavtseva and Lawson. Our technique builds on the usual constructions relating inverse semigroups with ample topological groupoids via germs and slices. Comment: 39 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.22181 Zobrazit plný text záznamu View this record from Arxiv