Bonn Topology Group - Abstracts
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Talk
MICHAEL BATANIN (Sydney, MPIM): Colimits of algebras over polynomial monads (17 April 2012)
Abstract
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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