## Internal algebras classifiers of polynomial monads and homotopy pushouts

### Michael Batanin – 2 August 2017

We investigate how internal algebras classifiers construction interacts with pushouts of polynomial monads. We observe that many classical constructions of homotopy theory of small categories (Quillen theorem A, Grothendieck construction, Thomason theorem etc.) can be generalised to polynomial monads using the language of classifiers

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