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 ∂-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.
Universal cohomology theories / L. Barbieri-Viale. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - 51:8(2023), pp. 3314-3345. [10.1080/00927872.2023.2181967]
Universal cohomology theories
L. Barbieri-Viale
2023
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 ∂-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.File | Dimensione | Formato | |
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