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Internal algebra classifiers and their applications

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If you have a question about this talk, please contact Julia Goedecke.

Given a map between two 2-monads S and T one can define a notion of internal S-algebra inside a T-algebra. For example, the category of monoids in a symmetric monoidal category is the category of internal algebras of the free monoidal category monad inside an algebra of the free symmetric monoidal category monad. The category of internal algebras form a 2-functor which is representable under some conditions on S and T. The representing object is called internal S-algebra classifier inside T-algebras. These internal algebra classifiers have remarkable properties which often allow to compute explicitly left adjoint functors between categories of algebras. This technique has numerous applications ranging from the construction of free monads in double categories and the explicit calculation of various envelopes of operads and PRO Ps to the construction of transferred model structures.

This talk is part of the Category Theory Seminar series.

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