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Barcelona Algebraic Topology Group

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Barcelona Algebraic Topology Group
Friday's Topology Seminar 2016-2017 PDF Print E-mail

Speaker: David White (Denison University)
Title:
Model Categories and the Grothendieck Construction
Place: Seminari C3b
Date:
23rd June at 12:00.
Abstract:
I will report on joint work with Michael Batanin studying the homotopy theory of the Grothendieck construction, given a category B and a functor F from B to CAT. From the Grothendieck construction we produce a “horizontal" model structure on the base B and “vertical” model structures on the fibers F(b). I will focus on examples, including pairs (R,A) where R is a (commutative) monoid and A is an R-module, pairs (P,A) where P is a (symmetric or non-symmetric) colored operad and A is a P-algebra, and pairs (T,A) where T is a 2-monad on Cat with rank and A is a T-algebra. I will also discuss how to get a semi-model structure under extremely general conditions. Additionally, we study when these model structures are left proper, and when a weak equivalence in B gives rise to a Quillen equivalence of fibers. Applications include change of rings, rectification of operad-algebras, strictification for categorical structures, and preservation of algebraic structure under left Bousfield localization. I will also explain the relationship of this work to that of Harpaz and Prasma.


Speaker: Rune Haugseng (Københavns Universitet)
Title: Enriched infinity-operads
Place: Seminari C3b
Date:
23rd June at 14:30.
Abstract:
I will discuss joint work with Hongyi Chu setting up foundations for a theory of enriched infinity-operads. In cases of interest such as spectral operads and dg-operads this recovers the usual homotopy theory of enriched operads, but is far better behaved - for example, there are natural infinity-categories of algebras over enriched infinity-operads. Time permitting, I will also discuss work in progress describing enriched infinity-operads as monoids in symmetric sequences; this will hopefully be a good setting for understanding Koszul duality beyond characteristic zero.

See the calendar for upcoming events.

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Presentation

This is the web site of the Algebraic Topology Team in Barcelona (Grup de Topologia Algebraica de Barcelona, 2014SGR-42 and Homotopy theory of algebraic structures, MTM2016-80439-P).

Our research interests include a variety of subjects in algebraic topology, group theory, homological algebra, and category theory. Here you will find information about us and our common activities.

 

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