We provide a correspondence between one-sided coideal subrings and one-sided ideal two-
sided coideals in an arbitrary bialgebroid. We prove that, under some expected additional …

Given a finitely generated and projective Lie–Rinehart algebra, we show that there is a
continuous homomorphism of complete commutative Hopf algebroids between the …

We build on our construction of Hopf algebroids from noncommutative calculi under the
further assumption of surjectivity for the calculus. We also introduce the notions of Hopf …

Mackey formula for bisets over groupoids Page 1 Journal of Algebra and Its Applications Vol.
18, No. 6 (2019) 1950109 (35 pages) c World Scientific Publishing Company DOI: 10.1142/S0219498819501093 …

In this paper we investigate the formal notions of differentiation and integration in the context
of commutative Hopf algebroids and Lie algebroid, or more precisely Lie-Rinehart algebras …

A fundamental tool of Differential Galois Theory is the assignment of an algebraic group to
each finite-dimensional differential module over differential field in such a way that the …

In the first part, we show in detail that difference Picard-Vessiot Galois theory is an instance
of Janelidze's categorical Galois theory. The same is true for Takeuchi's more general Hopf …

We construct a contravariant functor (the finite dual functor) from the category of co-
commutative Hopf algebroids to the category of commutative Hopf algebroids. Using this …

Given a morphism of (small) groupoids with injective object map, we provide sufficient and
necessary conditions under which the induction and co-induction functors between the …

We explore the concept of conjugation between subgroupoids, providing several
characterizations of the conjugacy relation (Theorem A in § 1.2). We show that two finite …