On invariant multiplications in a category
On inverse categories with split idempotents
We present some special properties of inverse categories with split idempotents. First, we examine a Clifford-Leech type theorem relative to such inverse categories. The connection with right cancellative categories with pushouts is illustrated by simple examples. Finally, some basic properties of inverse categories with split idempotents and kernels are studied in terms of split idempotents which generate (right or left) principal ideals of annihilators.
On Inverse Limit Of Function Spaces
On involutions of iterated bundle functors
We introduce the concept of an involution of iterated bundle functors. Then we study the problem of the existence of an involution for bundle functors defined on the category of fibered manifolds with m-dimensional bases and of fibered manifold morphisms covering local diffeomorphisms. We also apply our results to prolongation of connections.
On K2 of Finite Dimensional Division Algebras Over Arithmetical Fields.
On Kan fibrations for Maltsev algebras.
On Kurosh-Amitsur radicals of finite groups.
On Leibniz homology
We describe a spectral sequence for computing Leibniz cohomology for Lie algebras.
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 Limit Permanence of Projectivity and Ingectivity
On limits and colimits in the Kleisli category
On locally simply connected toposes and their fundamental groups
On locally small based algebraic theories
On long exact -sequences in module theory.
On Mackey topologies in topological abelian groups.
On measures in fibre spaces
On minimal realizations of behavior maps in categorial automata theory
On *-modules generating the injectives
On monadic quantale algebras: basic properties and representation theorems
Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.
On -exact categories
An -exact category is a pair consisting of an additive category and a class of sequences with terms satisfying certain axioms. We introduce -weakly idempotent complete categories. Then we prove that an additive -weakly idempotent complete category together with the class of all contractible sequences with terms is an -exact category. Some properties of the class are also discussed.