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- W3164196603 abstract "AbstractAbstractWe 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.Keywords: Cohomology theorymotives2020 Mathematics Subject Classification: 14F9918G6055N3503C60 AcknowledgmentsI am happy to express my thanks to Joseph Ayoub whose advice, interest and criticism were the indispensable ingredients for the writing of this paper. I’m also deeply grateful to Mike Prest for his constant help and precious collaboration. I also would like to dedicate this paper to the memory of V. Voevodsky, A. Grothendieck and S. Eilenberg to whom I’m intellectually tied and feel beholden. Finally, I also like to thank UZH & FIM–ETH Zürich for providing support, hospitality and excellent working conditions." @default.
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- W3164196603 date "2023-03-01" @default.
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- W3164196603 title "Universal cohomology theories" @default.
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- W3164196603 doi "https://doi.org/10.1080/00927872.2023.2181967" @default.
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