Localizations of exact and one-sided exact categories.
Adam-Christiaan van Roosmalen (Hasselt University, Belgium)
Abstract: Quotients of abelian and triangulated categories are ubiquitous in geometry, representation theory, and K-theory. In recent research, we consider quotients of exact categories by percolating subcategories. This approach extends earlier localization theories for exact categories by Cardenas and Schlichting, allowing new examples.
We obtain the quotient of an exact category E by a percolating subcategory A in two steps. In the first step, we localize the exact category E at a class of morphisms S_A. In general, this localization need not be an exact category, but merely one-sided exact. In the second step, one can obtain the quotient E/A as the exact hull of the localization. Furthermore, the quotient functor E --> E/A induces a Verdier localization on the level of the bounded derived categories.
In this talk, I will discuss this quotient construction and briefly discuss some applications and examples.
(Based on joint work with Ruben Henrard.)
combinatoricscategory theoryrings and algebrasrepresentation theory
Audience: researchers in the topic
( slides )
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