Post #1816215
2026-02-19 09:36 UTC
@dwarn There many more varieties of topological algebras that have that property. Universal algebra later established a condition SD(∧), i.e., varieties with *meet semidistributive congruence lattices*, that precisely describes those varieties.
Essentially, Taylor techniques show that any equation, that is satified by the algebra, has to be satisfied by its homotopy groups. There are no non-trivial models for an SD(∧) variety in groups.
Replies (1)
-
@dwarn@mathstodon.xyz 2026-02-19 10:17
@jakub_et_al Thanks for the reference. Indeed this seems closely related. I guess it's not exactly the same, since in the topological setting you get for free that the homotopies witnessing equations are based. But that's an reasonable assumption to add also in the homotopical setting.