?? monoid presented by generators g_abc with a,b,c in {0,1} and relators given by ... ???

?? 4 relators??

g_000 * g_100 = g_001 * g_110

"g_0ab * g_1bc is independent of b" ??? ...

??most obvious (for me at the moment) example of monoid with geometric realization having non-trivial higher homotopy groups ... ??? ....

?? morse-segal category (in this case poset ...) of generic ellipsoid ... ????... ??? "2-globe" / "bihedron" ...

??pre-sheaves on morse-segal categories ... ???.... hmmm ... ??? lawvere ... joyal ... ???... freyd ... ??...

???morse-segal categories (??of certain posets especially ??? ...) and ... a-series schubert-galois connection ... ????.... ??? ...

pi_1 as ... ???free on 5 generators ??? ... ???hmmm, so is it sort of like there's a redundancy among the 4 relators that manifests as an element of pi(2) ??? ...