Timeline for Path components of a monoidal category acting on homology
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 27, 2013 at 1:42 | vote | accept | Joshua Seaton | ||
| Apr 27, 2013 at 1:42 | comment | added | Joshua Seaton | Got it - thanks for the clarification. Accepted. | |
| Apr 27, 2013 at 1:24 | comment | added | Geoffroy Horel | The geometric realization of a simplicial set is a CW-complex so it is certainly compactly generated. But you don't even need that. It's perfectly fine to define homology of a simplicial set by applying the free abelian group functor degreewise and then take the alternating sum of the faces as differential and take homology of the resulting chain complex. | |
| Apr 26, 2013 at 22:01 | comment | added | Joshua Seaton | Sorry for the delay. -- You write that geometric realisation is product-preserving. The resources I've checked though say that this is not true in general, but is true when the spaces involved are compactly-generated. Am I missing something? | |
| Apr 1, 2013 at 18:32 | comment | added | Geoffroy Horel | Done. Let me know if you would like to see more details. | |
| Apr 1, 2013 at 18:31 | history | edited | Geoffroy Horel | CC BY-SA 3.0 |
added 551 characters in body
|
| Apr 1, 2013 at 1:16 | comment | added | Joshua Seaton | @Geoffroy: May you please elaborate on the first point. And by 'at the level of p-simplices' do you mean within the nerve or within the classifying space? | |
| Mar 31, 2013 at 19:53 | history | answered | Geoffroy Horel | CC BY-SA 3.0 |