  In this paper, we compute the posets of wide subcategories and ICE-closed
subcategories from the lattice of torsion classes in an abelian length category
in a purely lattice-theoretical way, by using the kappa map in a completely
semidistributive lattice. As for the poset of wide subcategories, we give two
more simple constructions via a bijection between wide subcategories and
torsion classes with canonical join representations. More precisely, for a
completely semidistributive lattice, we give two poset structures on the set of
elements with canonical join representations: the kappa order (defined using
the extended kappa map of Barnard--Todorov--Zhu), and the core label order
(generalizing the shard intersection order for congruence-uniform lattices).
Then we show that these posets for the lattice of torsion classes coincide and
are isomorphic to the poset of wide subcategories. As a byproduct, we give a
simple description of the shard intersection order on a finite Coxeter group
using the extended kappa map.
