On ℤ/2ℤ-extensions of pointed fusion categories
We give a classification of ℤ/2ℤ-graded fusion categories whose 0-component is a pointed fusion category. A number of concrete examples are considered.
On a theory of braided cochains in algebraic topology (Preliminary version). (Sur une théorie des cochaines tresses en topologie algébrique (Version préliminaire ).)
On *-autonomous categories of topological modules.
On *-autonomous categories of topological vector spaces
On braiding, syllapses and symmetries
On categorical crossed modules.
On clones of relations
On cohomology of graded group categories
On endomorphism algebras of separable monoidal functors.
On extensions of lax monads.
On filtered weighted colimits of presheaves
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 generalized Hom-functors of certain symmetric monoidal categories
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 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 braiding on a Hopf algebra in a braided category.
On the homotopy transfer of structures
The present article is devoted to the study of transfers for structures, their maps and homotopies, as developed in [7]. In particular, we supply the proofs of claims formulated therein and provide their extension by comparing them with the former approach based on the homological perturbation lemma.
On the corresponding to bialgebras
On the structure of halfdiagonal-halfterminal-symmetric categories with diagonal inversions
The category of all binary relations between arbitrary sets turns out to be a certain symmetric monoidal category Rel with an additional structure characterized by a family of diagonal morphisms, a family of terminal morphisms, and a family of diagonal inversions having certain properties. Using this properties in [11] was given a system of axioms which characterizes the abstract concept of a halfdiagonal-halfterminal-symmetric monoidal category with diagonal inversions (hdht∇s-category)....
Operads in iterated monoidal categories.