Post #1815123
2026-04-25 01:16 UTC
The kernel of a group homomorphism phi : G -> H has a universal property in the category of groups: it's the equalizer of phi and the 0 morphism.
It also has a universal property in the category of subgroups displayed over the category of groups: it is the cartesian lift along phi of the trivial subgroup { e } of H.
Replies (1)
-
@pamorim@mathstodon.xyz 2026-04-25 09:41
@maxsnew by the category of subgroups displayed over groups do you mean the Grothendieck construction of the presheaf on the category of groups that maps every group to its subgroups?