J.-L. Loday has defined generalised bialgebras and proved structure theorems in this setting
which can be seen as general forms of the Poincaré–Birkhoff–Witt and the Cartier–Milnor …

We survey the theory of Hopf monads on monoidal categories, and present new examples
and applications. As applications, we utilise this machinery to present a new theory of cross …

A categorified version of Hilbert's Theorem 90 is given. The natural setting for our result is
that of symmetric monoidal categories. Some applications to the symmetric monoidal …

For a generalisation of the classical theory of Hopf algebra over fields, A. Brugui\eres and A.
Virelizier study opmonoidal monads on monoidal categories (which they called {\em …

One reason for the universal interest in Frobenius algebras is that their characterisation can
be formulated in arbitrary categories: a functor K: A→ B between categories is Frobenius if …

The zeroth and first descent cohomology sets for a (co) monad on arbitrary base category
with coefficients in a (co) algebra are introduced and their basic properties are studied …

The theories of (Hopf) bialgebras and weak (Hopf) bialgebras have been introduced for
vector space categories over fields and make heavily use of the tensor product. As first …

As shown in a previous paper by the same authors, the theory of Galois functors provides a
categorical framework for the characterisation of bimonads on any category as Hopf monads …

Processes are often viewed as coalgebras, with the structure maps specifying the state
transitions. In the simplest case, the state spaces are discrete, and the structure map simply …

Given a monad and a comonad, one obtains a distributive law between them from lifts of one
through an adjunction for the other. In particular, this yields for any bialgebroid the Yetter …