Axioms for Bockstein homomorphisms
Chain functors with isomorphic homology.
Chain theories and simplicial abelian group spectra.
Coarse homology theories.
Cohomology theories on compact and locally compact spaces.
This paper is devoted to an exposition of cohomology theories on categories of spaces where the cohomology theories satisfy the type of axiom system considered in [1, 12, 16, 17, 18]. The categories considered are Ccomp, the category of all compact Haudorff spaces and continuous functions between them, and Cloc comp, the category of all locally compact Hausdorff spaces and proper continuous functions between them. The fundamental uniqueness theorem for cohomology theories on a finite dimensional...
Comparing homologies: Cech's theory, singular chains, integral flat chains and integral currents.
Comparison of Taut Cohomologies
Generalized differential forms over an operand and algebraic models of fibrations. (Formes différentielles généralisées sur une opérade et modéles algébriques des fibrations.)
Homology with models
Natural factorizations and the Kan extension of cohomology theories
On the categorical foundations of homological and homotopical algebra
The homotopy axiom in semialgebraic cohomology.
Théories cohomologiques.
Topos based homology theory
In this paper we extend the Eilenberg-Steenrod axiomatic description of a homology theory from the category of topological spaces to an arbitrary category and, in particular, to a topos. Implicit in this extension is an extension of the notions of homotopy and excision. A general discussion of such homotopy and excision structures on a category is given along with several examples including the interval based homotopies and, for toposes, the excisions represented by “cutting out” subobjects. The...
Weakly additive cohomology.
In this paper the concept of weakly additive cohomology theory is introduced as a variant of the known concept of additive cohomology theory. It is shown that for a closed A in X the singular homology of the pair (X, X-A) (with some fixed cohomology group) regarded as a furcter of A is a weakly additive cohomology theory on any collectionwise normal space X. Furthermore, every compactly supported cohomology theory is weakly additive.The main result is a comparison theorem for two cohomology theories...
Гипергомологии предела прямого спектра комплексов и группы гомологий топологических пространств
Об аксиомах теории гомологий
Отображения спектральных последовательностей и обобщенная аксиома гомотопии.
Условие эквивалентности гомологических теорий на категории бикомпактов