Timeline for Evaluation functors and injective model structure on diagram categories
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 29, 2012 at 16:33 | comment | added | The mathwalker | Fabian, when you write $End_C(b,c)$ do you mean $Hom(b,c)$ ? If so, the hypothesis that there is a unique morphism between any two objects, means that $Hom(b,c)$ is just a one-element set so the coproduct reduces to one object. If C is like EG which is a groupoid, the image of C must lie in the biggest groupoid contained in $M$ (some people call it the interior of $M$). It's like a representation of G. So I don't know if your structure map $L(c) \to L(c') $ is invertible in $M$. What do you think ? | |
| Mar 29, 2012 at 12:51 | vote | accept | The mathwalker | ||
| Mar 29, 2012 at 12:51 | |||||
| Mar 29, 2012 at 12:49 | comment | added | The mathwalker | Thanks again, that helps ! I think the type of categories you're describing correspond to either a posetal category or the indiscrete category associated to a set $S$; it's a groupoid like EG for a group G. In fact it's isomorphic to some EG. | |
| Mar 29, 2012 at 9:39 | history | edited | Fabian Lenhardt | CC BY-SA 3.0 |
added 2 characters in body
|
| Mar 29, 2012 at 9:07 | history | answered | Fabian Lenhardt | CC BY-SA 3.0 |