From the lattice of torsion classes to wide and ICE-closed subcategories

Date:

Seminar Talk in BIREP Seminar at Online

Based on my preprint:

Abstract

For a module category, we can consider the posets of various subcategories. In this talk, I explain that we can compute the posets of wide and ICE-closed (Image, Cokernel, Extension-closed) subcategories from the lattice of torsion classes in a purely combinatorial way. Also I give a simple expression of the poset of wide subcategories from the lattice of torsion classes, and give an application to the combinatorics of Reading’s shard intersection order on Coxeter groups.

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