Universal cohomology theories

Abstract

We furnish any category of a universal (co)homology theory. Universal (co)homologies and universal relative (co)homologies are obtained by showing representability of certain functors and take values in $R$-linear abelian categories of motivic nature, where $R$ is any commutative unitary ring. Universal homology theory on the one point category yields "hieratic" $R$-modules, i.e. the indization of Freyd's free abelian category on $R$. Grothendieck $\partial$-functors and satellite functors are recovered as certain additive relative homologies on an abelian category for which we also show the existence of universal ones.

References added

References in corpus (3)

• Tensor structure for Nori motives
• Tensor product of motives via Künneth formula
• On topological motives

Cited by in corpus (2)

• On topological motives
• Motives