Based on my preprint:
- From the lattice of torsion classes to the posets of wide subcategories and ICE-closed subcategories
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.