A Leibniz algebra structure on the second tensor power.
A lifting theorem for right adjoints
A logic of injectivity.
A logic of orthogonality
A logic of orthogonality characterizes all “orthogonality consequences" of a given class of morphisms, i.e. those morphisms such that every object orthogonal to is also orthogonal to . A simple four-rule deduction system is formulated which is sound in every cocomplete category. In locally presentable categories we prove that the deduction system is also complete (a) for all classes of morphisms such that all members except a set are regular epimorphisms and (b) for all classes , without...
A Magnus-Witt type isomorphism for non-free groups.
A Maschke type theorem for relative Hom-Hopf modules
Let be a monoidal Hom-Hopf algebra and a right -Hom-comodule algebra. We first introduce the notion of a relative Hom-Hopf module and prove that the functor from the category of relative Hom-Hopf modules to the category of right -Hom-modules has a right adjoint. Furthermore, we prove a Maschke type theorem for the category of relative Hom-Hopf modules. In fact, we give necessary and sufficient conditions for the functor that forgets the -coaction to be separable. This leads to a generalized...
A matrix characterization of the maximal groups in
A metric tangential calculus.
A Model for Computing Rational Algebraic K-Theory of Simply Connected Spaces.
A monadic approach to polycategories.
A natural map from the ext Künneth sequence to the Tor one.
A new proof of Reiterman's theorem
A New Proof of the Eilenberg-Zilber-Cartier Theorem.
A non-abelian tensor product of Leibniz algebra
Leibniz algebras are a non-commutative version of usual Lie algebras. We introduce a notion of (pre)crossed Leibniz algebra which is a simultaneous generalization of notions of representation and two-sided ideal of a Leibniz algebra. We construct the Leibniz algebra of biderivations on crossed Leibniz algebras and we define a non-abelian tensor product of Leibniz algebras. These two notions are adjoint to each other. A (co)homological characterization of these new algebraic objects enables us to...
A Norm for Modules and Algebras.
A note monies and epics in varieties of categories
A note on actions of a monoidal category.
A note on algebraic categories
A note on categories enriched in quantaloids and modal and temporal logic
A note on categories of partial algebras