Ancestors

Written by Trebor on 2025-01-31 at 15:05

K(G,1) can be defined as the type of G-torsors, and addition corresponds to taking the tensor product (in the obvious way). So what's the multiplication when G is a ring?

=> More informations about this toot | More toots from trebor@types.pl

Written by Trebor on 2025-01-31 at 15:30

It's difficult to think about K(G,2) if it's defined as the truncation of suspension of K(G,1). Is there a better way?

=> More informations about this toot | More toots from trebor@types.pl

Written by daniel gratzer on 2025-01-31 at 17:33

@trebor So you can think of it as still classifying something like torsors, but now appropriately higher-dimensional. The relevant word here is "gerbe" (I think @buchholtz has a talk on such things in HoTT).

The fact that higher EM spaces classify n-gerbes is one of the results in higher topos theory (Theorem 7.2.2.26). It's also one of the motivations given in the preface, which is worth reading

=> More informations about this toot | More toots from danielgratzer@mathstodon.xyz

Toot

Written by Tom de Jong on 2025-01-31 at 17:41

@danielgratzer @trebor

Indeed @buchholtz does: https://youtu.be/eB6HwGLASJI

(See also Lemma 5.4 of our paper on acyclic types: https://arxiv.org/abs/2401.14106)

=> More informations about this toot | More toots from de_Jong_Tom@mathstodon.xyz

Descendants