Timeline for Construct a 'nice' trivializing cover of universal principal $G$-bundle $EG \to BG$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 18, 2023 at 6:09 | comment | added | Dmitri Pavlov | @JohnRognes: The canonical homeomorphism of Fritsch–Puppe (Theorem 4.6.4 in Fritsch–Piccinini's Cellular structures in topology). It is is functorial with respect to isomorphisms of simplicial sets, which is all what is necessary here. | |
| Jan 17, 2023 at 7:43 | comment | added | John Rognes | @DmitriPavlov What is the canonical homeomorphism from |Sd(Sd(X))| to |X| that you have in mind for X = *//G? There is no natural such homeomorphism, cf. Rudolf Fritsch, Zur Unterteilung semisimplizialer Mengen. I., Math. Z. 108 (1969), 329–367. | |
| Jan 17, 2023 at 2:31 | comment | added | Dmitri Pavlov | @user7391733: The notation // is just the action groupoid: ncatlab.org/nlab/show/action+groupoid. The nerve functor is the usual functor from small categories to simplicial sets. | |
| Jan 17, 2023 at 0:20 | comment | added | user267839 | could you loose some words on how to interpret the notation $\def\sq{/\!/} G\sq G→*\sq G$, ie what do you mean by this $A \sq B$ notation? Is this just some kind of "categorified" version of the usual nerve functor associating to a group a simplicial set? A naive guess: here you replace a usual group $G$ by a "group object" in some kind of fibered category (at least this object looks like one comming from there) and this "bulked" nerve functor maps to some kind functor with additional simplicial structure. Is this the rough idea behind this notation? | |
| Jan 16, 2023 at 20:44 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |