36 citations · 84 across the 14 of their papers we have counts for
8 papers · 1 filter
Correspondence theorems for Hopf algebroids with applications to affine groupoids
Laiachi El Kaoutit, Aryan Ghobadi, Paolo Saracco +1
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 con…
Finite dual of a cocommutative Hopf algebroid. Application to linear differential matrix equations and Picard-Vessiot theory
Laiachi El Kaoutit, José Gómez-Torrecillas
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 t…
Representative functions on discrete groupoids and duality with Hopf algebroids
Laiachi EL Kaoutit
The aim of this paper is to establish a duality between the category of discrete groupoids and the category of geometrically transitive commutative Hopf algebroids in the sense of…
Invertible Bimodules, Miyashita Action in Monoidal Categories and Azumaya Monoids
Alessandro Ardizzoni, Laiachi El Kaoutit
In this paper we introduce and study Miyashita action in the context of monoidal categories aiming by this to provide a common framework of previous studies in the literature. We m…
Invertible unital bimodules over rings with local units, and related exact sequences of groups II
L. EL Kaoutit, J. Gómez-Torrecillas
Let be a ring with a set of local units, and a homomorphism of groups $\underlineΘ : \G \to \Picar{R}$ to the Picard group of . We study under which conditions …
Categories of comodules and chain complexes of modules
A. Ardizzoni, L. El Kaoutit, C. Menini
Let $\lL(A)$ denote the coendomorphism left -bialgebroid associated to a left finitely generated and projective extension of rings with identities. We show that the ca…
The bicategories of corings
Tomasz Brzezinski, L El Kaoutit, J Gomez-Torrecillas
To a B-coring and a (B,A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a cor…
Semisimple corings
L. El Kaoutit, J. Gomez-Torrecillas, F. J. Lobillo
While semisimple artinian rings and semisimple coalgebras over a field can be described in terms of matrices (either matrix ring over division rings or comatrix coalgebras over the…