We introduce and investigate the properties of Hochschild cohomology of algebras in an
abelian monoidal category M. We show that the second Hochschild cohomology group of an …

Let H be a quasi-Hopf algebra. We apply results obtained in [8] to give necessary and
sufficient conditions for the forgetful functor from Doi–Hopf modules, two-sided Hopf …

The main goal of this paper is to investigate the structure of Hopf algebras with the property
that either its Jacobson radical is a Hopf ideal or its coradical is a subalgebra. Let us …

We continue our investigation of the general notion of universal enveloping algebra
introduced in [A. Ardizzoni, A Milnor–Moore type theorem for primitively generated braided …

Twisted separable functors generalize the separable functors of Nastasescu, Van den Bergh
and Van Oystaeyen, and provide a convenient tool to compare various projective …

Comodule algebras of a Hopf algebroid H with a bijective antipode, ie algebra extensions
B⊆ A by H, are studied. Assuming that a lifted canonical map is a split epimorphism of …

The notion of a formally smooth bimodule is introduced and its basic properties are
analyzed. In particular it is proven that a B–A bimodule M which is a generator left B-module …

We introduce the concept of cotensor coalgebra for a given bicomodule over a coalgebra in
an Abelian monoidal category ℳ. If ℳ is also cocomplete, complete, and AB5, we show that …

In this paper we associate to a k-qurve A (formerly known as a quasi-free algebra [J. Cuntz,
D. Quillen, Algebra extensions and nonsingularity, J. Amer. Math. Soc. 8 (1995) 251–289] or …

We show that, under some mild conditions, a bialgebra in an abelian and coabelian braided
monoidal category has a weak projection onto a formally smooth (as a coalgebra) sub …