On Double Dualization Monads.
On endomorphism algebras of separable monoidal functors.
On extensions of lax monads.
On filtered weighted colimits of presheaves
On functors from compact to Banach algebras
On functors which are lax epimorphisms.
On fuzzification of the notion of quantaloid
The paper considers a fuzzification of the notion of quantaloid of K. I. Rosenthal, which replaces enrichment in the category of -semilattices with that in the category of modules over a given unital commutative quantale. The resulting structures are called quantale algebroids. We show that their constitute a monadic category and prove a representation theorem for them using the notion of nucleus adjusted for our needs. We also characterize the lattice of nuclei on a free quantale algebroid. At...
On Galois -objects and invertible -modules
On generalized Hom-functors of certain symmetric monoidal categories
On generic separable objects.
On Lie algebras in braided categories
The category of group-graded modules over an abelian group is a monoidal category. For any bicharacter of this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have -ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are noncommutative...
On property-like structures.
On reflexive subobject lattices and reflexive endomorphism algebras
In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.
On regular presheaves and regular semi-categories
On some adjunctions between the categories of adjunction-morphisms and monad-morphisms
On some anticyclic operads.
On some properties of pure morphisms of commutative rings.
On superalgebras over operads.
On systems of linear inequalities
We show in detail that the category of general Roth systems or the category of semi-stable systems of linear inequalities of slope zero is a neutral Tannakian category. On the way, we present a new proof of the semi-stability of the tensor product of semi-stable systems. The proof is based on a numerical criterion for a system of linear inequalities to be semi-stable.
On the axiomatisation of Boolean categories with and without medial.