Free minimal resolutions and the Betti numbers of the suspension of an -gon.
From cubical to globular higher categories
Functors between homotopy theories
Fundamental pro-groupoids and covering projections
We introduce a new notion of covering projection E → X of a topological space X which reduces to the usual notion if X is locally connected. We use locally constant presheaves and covering reduced sieves to find a pro-groupoid π crs (X) and an induced category pro (π crs (X), Sets) such that for any topological space X the category of covering projections and transformations of X is equivalent to the category pro (π crs (X), Sets). We also prove that the latter category is equivalent to pro (π CX,...
Further remarks on systems of interlocking exact sequences.
Generalized Dehn-Sommerville equations and an upper bound theorem
Generalized homotopy in C-categories.
Generalized homotopy theory.
G-functors, G-posets and homotopy decompositions of G-spaces
We describe a unifying approach to a variety of homotopy decompositions of classifying spaces, mainly of finite groups. For a group G acting on a poset W and an isotropy presheaf d:W → (G) we construct a natural G-map which is a (non-equivariant) homotopy equivalence, hence is a homotopy equivalence. Different choices of G-posets and isotropy presheaves on them lead to homotopy decompositions of classifying spaces. We analyze higher limits over the categories associated to isotropy presheaves...
Global actions, groupoid atlases and applications.
Globular realization and cubical underlying homotopy type of time flow of process algebra.
Heaps and unpointed stable homotopy theory
In this paper, we show how certain “stability phenomena” in unpointed model categories provide the sets of homotopy classes with a canonical structure of an abelian heap, i.e. an abelian group without a choice of a zero. In contrast with the classical situation of stable (pointed) model categories, these sets can be empty.
Heller's axioms for homotopy theory
Higher cospans and weak cubical categories (cospans in algebraic topology. I).
Higher dimensional Peiffer elements in simplicial commutative algebras.
Higher fundamental functors for simplicial sets
Higher homotopy groupoids and Toda brackets.
Higher order relations for a numerical semigroup
Higher Torsion in SG and BSG.
Higher-dimensional algebra. VI: Lie 2-algebras.