University of Cambridge > Talks.cam > Category Theory Seminar > Internal algebra classifiers and their applications

Internal algebra classifiers and their applications

Add to your list(s) Download to your calendar using vCal

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.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2019 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity