Work

The Boolean spectrum of a Grothendieck category

Year: 2026

Type: article

Abstract: 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.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70719

Author: Henning Krause

Institution: Bielefeld University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: Deutsche Forschungsgemeinschaft