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Categories enriched over oplax monoidal categories
Thomas Basile, Damien Lejay, Kevin Morand
We define a notion of category enriched over an oplax monoidal category , extending the usual definition of category enriched over a monoidal category. Even though oplax monoida…
Base change along lax squares
Brice Le Grignou, Damien Lejay
In this note we present a recipe which transforms any pull-push along a span of categories into a push-pull along a cospan and vice versa, based on a theorem from Guitart.
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…
Exponentiable Higher Toposes
Mathieu Anel, Damien Lejay
We characterise the class of exponentiable -toposes: is exponentiable if and only if is a continuous -category. The…