Hurewicz isomorphism theorem for Steenrod homology

The Hurewicz Theorem

The fundamental group and homology groups both give extremely useful information, particularly about path-connected spaces. Both can be considered as functors, so we can use these constructional invariants as convenient guides to classifying spaces. However, though homology groups are often easy to compute, the fundamental group sometimes is not. In fact, it is often not even obvious when a spa...

Homology of Types in Model Theory Ii: a Hurewicz Theorem for Stable Theories

This is a sequel to the paper [6] ‘Homology of types in model theory I: Basic concepts and connections with type amalgamation’. We compute the group H2 for strong types in stable theories and show that any profinite abelian group can occur as the group H2 in the model-theoretic context. The work described in this paper was originally inspired by Hrushovski’s discovery [8] of striking connection...

Directed Homology Theories and Eilenberg-Steenrod Axioms

In this paper, we define and study a homology theory, that we call “natural homology”, which associates a natural system of abelian groups to every space in a large class of directed spaces and precubical sets. We show that this homology theory enjoys many important properties, as an invariant for directed homotopy. Among its properties, we show that subdivided precubical sets have the same hom...

On the Pontryagin-steenrod-wu Theorem

An isomorphism theorem for digraphs

A seminal result by Lovász states that two digraphs A and B (possibly with loops) are isomorphic if and only if for every digraph X the number of homomorphisms X → A equals the number of homomorphisms X → B. Lovász used this result to deduce certain cancellation properties for the direct product of digraphs. We develop an analogous result for the class of digraphs without loops, and with weak h...