The Boolean spectrum of a Grothendieck category

Autor:	Krause, Henning
Rok vydání:	2024
Předmět:	Mathematics - Category Theory Mathematics - Rings and Algebras Mathematics - Representation Theory 18E10 (primary) 16D70 16E50 18E40 18E45 (secondary)
Druh dokumentu:	Working Paper
Popis:	A notion of support for objects in any Grothendieck category is introduced. This is based on the spectral category of a Grothendieck category and uses its Boolean lattice of localising subcategories. The support provides a classification of all subcategories that are closed under arbitrary coproducts, subobjects, and essential extensions. There is also a notion of exact support which classifies certain thick subcategories. As an application, the coproduct decompositions of objects are described in terms of Boolean lattices. Also, for any ring Crawley-Boevey's correspondence between definable subcategories of modules and closed subsets of the Ziegler spectrum is extended. Comment: 26 pages. V2: Substantial revision, including a new section on coproduct decompositions
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.16309 Zobrazit plný text záznamu View this record from Arxiv