On algebraic models for homotopy 3-types.
On categorical crossed modules.
On ideals and homology in additive categories.
On n-permutable equivalence relations in regular categories
On reflective subcategories of quasiabelian categories.
On the classification of complex analytic supermanifolds.
On the cohomology sequence in a semiabelian category.
On the equivalence of Quillen's and Swan's -theories.
Protomodularity, descent, and semidirect products.
Quandle coverings and their Galois correspondence
This article establishes the algebraic covering theory of quandles. For every connected quandle Q with base point q ∈ Q, we explicitly construct a universal covering p: (Q̃,q̃̃) → (Q,q). This in turn leads us to define the algebraic fundamental group , where Adj(Q) is the adjoint group of Q. We then establish the Galois correspondence between connected coverings of (Q,q) and subgroups of π₁(Q,q). Quandle coverings are thus formally analogous to coverings of topological spaces, and resemble Kervaire’s...
Quasi-abelian categories and sheaves
Quillen cohomology and Baues-Wirsching cohomology of algebraic, theories
Relative homological categories.
Semidirect products of categorical groups. Obstruction theory.
Shimuravarietäten und Gerben.
Simplicial and crossed Lie algebras.
Some results on central extensions of crossed modules.
Split extensions and semidirect products of unitary magmas
We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivalence between the categories of split extensions and of (suitably defined) actions of unitary magmas on unitary magmas. The class of split extensions is pullback stable but not closed under composition. We introduce two subclasses of it that have both of these properties.
Stacks and the homotopy theory of simplicial sheaves.
Teisi in .