This is the first extensive treatment of the theory of corings and their comodules. In the first
part, the module-theoretic aspects of coalgebras over commutative rings are described …

It is a key property of bialgebras that their modules have a natural tensor product. More
precisely, a bialgebra over k can be characterized as an algebra H whose category of …

Skew-monoidal categories arise when the associator and the left and right units of a
monoidal category are, in a specific way, not invertible. We prove that the closed skew …

We define Hopf monads on an arbitrary monoidal category, extending the definition given in
Bruguières and Virelizier (2007)[5] for monoidal categories with duals. A Hopf monad is a …

Module theory over commutative asociative rings is usually extended to noncommutative
associative rings by introducing the category of left (or right) modules. An alternative to this …

Why are groupoids such special categories? The obvious answer is because all arrows
have inverses. Yet this is precisely what is needed mathematically to model symmetry in …

We introduce and study Hopf monads on autonomous categories (ie, monoidal categories
with duals). Hopf monads generalize Hopf algebras to a non-braided (and non-linear) …

We show that the well-known Morita theorems on equivalences of categories of modules
hold true of categories of comodules over a field k. We go parallel with| H. Bass, Algebraic K …

Let C be a cocomplete monoidal category such that the tensor product in C preserves
colimits in each argument. Let A be an algebra in C. We show (under some assumptions …