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On the 2-categories of weak distributive laws
Gabriella Böhm, Stephen Lack, Ross Street
A weak mixed distributive law (also called weak entwining structure) in a 2-category consists of a monad and a comonad, together with a 2-cell relating them in a way which generali…
Enriched weakness
Stephen Lack, Jiri Rosicky
The basic notions of category theory, such as limit, adjunction, and orthogonality, all involve assertions of the existence and uniqueness of certain arrows. Weak notions arise whe…
Hopf monads on monoidal categories
Alain Bruguières, Steve Lack, Alexis Virelizier
We define Hopf monads on an arbitrary monoidal category, extending the definition given previously for monoidal categories with duals. A Hopf monad is a bimonad (or opmonoidal mona…
Hopf monoidal comonads
Dimitri Chikhladze, Stephen Lack, Ross Street
Alain Bruguieres, in his talk [1], announced his work [2] with Alexis Virelizier and the second author which dealt with lifting closed structure on a monoidal category to the categ…
A Quillen model structure for Gray-categories
Stephen Lack
A Quillen model structure on the category Gray-Cat of Gray-categories is described, for which the weak equivalences are the triequivalences. It is shown to restrict to the full sub…
Weak bimonads and weak Hopf monads
Gabriella Böhm, Stephen Lack, Ross Street
We define a weak bimonad as a monad T on a monoidal category M with the property that the Eilenberg-Moore category M^T is monoidal and the forgetful functor from M^T to M is separa…