Universal cohomology theories

Cohomology Theories

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Eqüivariant Cohomology Theories

Throughout this note G denotes a discrete group. A G-complex is a CPP-complex on which G acts by cellular maps such that the fixed point set of any element of G is a subcomplex. On the category of pairs of G-complexes and equivariant homotopy classes of maps, an equivariant cohomology theory is a sequence of contravariant functors 3C into the category of abelian groups together with natural tra...

Cohomology of Algebraic Theories

Generalised sheaf cohomology theories

This paper is an expanded version of notes for a set of lectures given at the Isaac Newton Institute for Mathematical Sciences during a NATO ASI Workshop entitled “Homotopy Theory of Geometric Categories” on September 23 and 24, 2002. This workshop was part of a program entitled New Contexts in Stable Homotopy Theory that was held at the Institute during the fall of 2002. The intent for the lec...

Cohomology Theories on Spaces E

In this paper a previously proven uniqueness theorem for nonnegative cohomology theories on the same space is extended to cohomology theories on the same finite-dimensional space. In this form it is applicable to extraordinary cohomology theories. An example is given to show that the theorem does not hold without finite dimensionality.