Algebr Represent Theor (2018) 21:551–563
Classifying Dense Resolving and Coresolving
Subcategories of Exact Categories Via Grothendieck
Received: 1 February 2017 / Accepted: 20 July 2017 / Published online: 29 July 2017
© Springer Science+Business Media B.V. 2017
Abstract Classification problems of subcategories have been deeply considered so far. In
this paper, we discuss classifying dense resolving and dense coresolving subcategories of
exact categories via their Grothendieck groups. This study is motivated by the classification
of dense triangulated subcategories of triangulated categories due to Thomason.
Keywords Exact category · Dense subcategory · Resolving subcategory · Coresolving
subcategory · Grothendieck group
Mathematics Subject Classification (2010) 18E10 · 18F30 · 16G50
be a category. Classifying subcategories means for a property P, finding a one-to-one
where the set S is easier to understand. Classifying subcategories is an important approach
to understand the category
and has been studied in various areas of mathematics, for exam-
ple, stable homotopy theory, commutative/noncommutative ring theory, algebraic geometry,
and modular representation theory.
Presented by Henning Krause.
The author is supported by Grant-in-Aid for JSPS Fellows 16J01067.
Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku,
Nagoya, Aichi 464-8602, Japan