Timeline for Is dgCat a category or a 2-category?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 20, 2015 at 1:58 | vote | accept | Zhaoting Wei | ||
| Oct 14, 2015 at 9:28 | history | edited | AAK | CC BY-SA 3.0 |
added 260 characters in body
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| Oct 14, 2015 at 8:36 | comment | added | AAK | Any model category (in fact, even just a category with weak equivalences) gives rise to an $(\infty,1)$-category. For example, if one takes simplicially enriched categories as a model of $(\infty,1)$-categories, this is given by the Dwyer-Kan simplicial localization. | |
| Oct 14, 2015 at 2:00 | comment | added | Zhaoting Wei | @Adeel Could you explain a little bit what does it mean by The model structure on the category of dg-categories "presents" an $(\infty,1)$=category DGCAT? | |
| Sep 29, 2015 at 8:08 | comment | added | AAK | @ZhenLin: Gepner-Haugseng show that the $\infty$-category of $V$-enriched $\infty$-categories has an enrichment over itself, for $V$ a presentably $E_2$-monoidal $\infty$-category. In particular this gives the enrichment of DGCat over itself, and hence via Dold-Kan an enrichment over $\infty$-categories. (I'm using implicitly the rectification result of Haugseng, which implies that DGCat is equivalent to the $\infty$-category of $\infty$-categories enriched over the $\infty$-category of chain complexes.) | |
| Sep 29, 2015 at 7:47 | comment | added | Zhen Lin | Can we construct an "actual" $(\infty, 2)$-category, say a $\Theta_2$-space or a quasicategory-enriched category? After all, there are such things as sesquicategories which have hom-categories but otherwise fail to completely satisfy the 2-category axioms. | |
| Sep 29, 2015 at 7:42 | history | answered | AAK | CC BY-SA 3.0 |