Bonn Topology Group - Abstracts

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MICHAEL BATANIN (Sydney, MPIM): Colimits of algebras over polynomial monads (17 April 2012)


Polynomial monads and their algebras are abundant in nature. Monoids, symmetric and nonsymmetric operads, properads, PROPs, cyclic and modular operads, n-operads are examples of algebras of polynomial monads. We show that colimits (more generally left Kan extensions) of algebras of polynomial monads can be calculated in terms of ordinary colimits in a universal way.
Among many applications of this techniques we consider a generalisation of Schwede and Shipley construction for calculation of pushouts along free maps. This construction plays a crucial role in the existence (and properties) of model structure on the category of algebras of a polynomial monad.
This is joint work with Mark Weber and Clemens Berger. The model theoretic aspects of this work will be a subject of Clemens Berger's talk.

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