A functor-valued invariant of tangles.
A Galois theory with stable units for simplicial sets.
A Generalization of Baer's Lemma
There is a classical result known as Baer’s Lemma that states that an -module is injective if it is injective for . This means that if a map from a submodule of , that is, from a left ideal of to can always be extended to , then a map to from a submodule of any -module can be extended to ; in other words, is injective. In this paper, we generalize this result to the category consisting of the representations of an infinite line quiver. This generalization of Baer’s Lemma...
A geometric decomposition of spaces into cells of different types.
A higher dimensional homotopy sequence.
A homological algebra for valuated groups
A homological characterization of graded complete intersections, II
A Homological Finiteness Criterion.
A Leibniz algebra structure on the second tensor power.
A Magnus-Witt type isomorphism for non-free groups.
A natural map from the ext Künneth sequence to the Tor one.
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 on exactness and stability in homotopical algebra.
A note on free regular and exact completions and their infinitary generalizations.
A note on Hacque's cohomology of rings-groups and extensions of rings-groups by groups.
A note on product structures on Hochschild homology of schemes
We extend the definition of Hochschild and cyclic homologies of a scheme over a commutative ring k to define the Hochschild homologies HH⁎(X/S) and cyclic homologies HC⁎(X/S) of a scheme X with respect to an arbitrary base scheme S. Our main purpose is to study product structures on the Hochschild homology groups HH⁎(X/S). In particular, we show that carries the structure of a graded algebra.
A Note on the Structure of Injective Diagrams.
A remark on Koszul complexes.
A Remark on Projective Dimension of Fiat Modules.