The quasi-category of homotopy coherent monads in a (∞, 2)-category.
Event details
| Date | 08.11.2016 |
| Hour | 10:15 › 11:30 |
| Speaker |
Dimitri Zaganidis (EPFL) |
| Location |
CM113
|
| Category | Conferences - Seminars |
Homotopy coherent diagrams in a simplicial category K can be encoded as simplicial functors C → K, where C is a well chosen simplicial category. This idea goes back at least to Cordier and Porter (Math. Proc. Cambridge Philos. Soc. 1986) and originated in earlier work of Vogt (Math. Z. 134, 1973) on homotopy coherent diagrams. For instance, the homotopy coherent nerve is constructed in this way. In Riehl and Verity’s paper (Adv. Math. 2016), C is the universal 2-category containing the object of study, either a monad or an adjunction. For instance they define homotopy coherent monads as simplicial functors Mnd → K, where K = qCat∞ , the category of quasi-categories enriched over itself, and where Mnd is the universal 2-category containing a monad.
In this talk, we define a cosimplicial object Mnd[-] in 2-categories which induces a nerve N_Mnd : sCat → sSet. When K is a 2-category, N_Mnd(K) = N(Mnd(K)), where Mnd(K) is the 1-category of monads in K, as defined by Street in (JPAA 1972). We will sketch the proof that when K is enriched in quasi-categories and sufficiently complete, NMnd (K) is a quasi-category whose objects are the homotopy coherent monads in K.
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Practical information
- Informed public
- Free
Organizer
- Magdalena Kedziorek