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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)
Model Categories and the Grothendieck Construction
Place: Seminari C3b
23rd June at 12:00.
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
23rd June at 14:30.
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.


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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