Timeline for Classifying space BG and contractable space EG
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 3, 2020 at 18:55 | comment | added | Dmitri Pavlov | @MortyPB: A natural transformation F→G (in our case, F=G//G→*→G//G and G=id) is a collection of morphisms F(X)→G(X) that satisfies a certain commutativity condition. The data of morphisms F(X)→G(X) is uniquely prescribed because we already know F(X) and G(X) and there is exactly one morphism of the form F(X)→G(X). Likewise, any square diagram (in fact, any diagram) in G//G automatically commutes because any pair of morphisms between the same objects coincides. | |
| Feb 3, 2020 at 16:39 | comment | added | user267839 | Could you lose few words on your last argument that the composition G//G→*→G//G is homotopic to identity "via the unique choices of morphisms in G//G". I not fully understand what you mean. By constuction between every $g,h \in G//G$ there exist exactly one map. Why does this imply the desired claim? | |
| Feb 3, 2020 at 16:32 | vote | accept | user267839 | ||
| Feb 3, 2020 at 3:22 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |