Timeline for A combinatorial approximation functor sSet->qCat
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 13, 2020 at 19:19 | answer | added | Dmitri Pavlov | timeline score: 8 | |
| Feb 14, 2018 at 20:11 | comment | added | Harry Gindi | The preservation of those products is easy to prove since $\mathbf{Ex}^n(A \times B)=\mathbf{Ex}^n(A)\times \mathbf{Ex}^n(B)$ for finite n, and then filtered colimits are universal in $\operatorname{sSet}$, so you get preservation of finite products. That makes it a monoidal functor, so it lifts to the enriched categories, and the induced maps are D-K equivalences (they are equivalences on Homs and bijections on objects). A simplicially enriched category is fibrant iff all of its Hom objects are Kan complexes, so we are done. | |
| Feb 14, 2018 at 19:57 | comment | added | Harry Gindi | @StephenNand-Lal If I remember correctly, this comes from the fact that $\operatorname{Ex}^\infty$ preserves finite products and the induced map is a Dwyer-Kan weak equivalence to a fibrant object. | |
| Feb 14, 2018 at 17:07 | comment | added | Stephen Nand-Lal | Do you have a reference for the claim in the category of simplicial categories? | |
| Jan 16, 2011 at 6:19 | history | edited | Harry Gindi | CC BY-SA 2.5 |
added 89 characters in body
|
| Jan 16, 2011 at 4:28 | history | edited | Harry Gindi | CC BY-SA 2.5 |
added 20 characters in body
|
| Jan 16, 2011 at 3:09 | history | edited | Harry Gindi |
edited tags
|
|
| Jan 16, 2011 at 2:59 | history | edited | Harry Gindi | CC BY-SA 2.5 |
added 3 characters in body
|
| Jan 16, 2011 at 2:46 | history | edited | Harry Gindi | CC BY-SA 2.5 |
added 237 characters in body; added 25 characters in body
|
| Jan 16, 2011 at 2:40 | history | asked | Harry Gindi | CC BY-SA 2.5 |