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Endomorphism operads of functors
Gabriel C. Drummond-Cole, Joseph Hirsh, Damien Lejay
We consider the endomorphism operad of a functor, which is roughly the object of natural transformations from (monoidal) powers of that functor to itself. There are many examples f…
Representations are adjoint to endomorphisms
Gabriel C. Drummond-Cole, Joseph Hirsh, Damien Lejay
The functor that takes a ring to its category of modules has an adjoint if one remembers the forgetful functor to abelian groups: the endomorphism ring of linear natural transforma…
Operads without coalgebras
Brice Le Grignou, Damien Lejay
We give an example of a non-trivial linear operad that only admits trivial coalgebras and give sufficient conditions ensuring that the cofree coalgebra functor be faithful.