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arXiv · 2105.13286

Universal cohomology theories

L. Barbieri-Viale
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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.

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L. Barbieri-Viale. 2021-05-27. Universal cohomology theories. https://doi.org/10.1080/00927872.2023.2181967

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