JournalsdmVol. 27pp. 699–717

A universal rigid abelian tensor category

  • Luca Barbieri-Viale

    Dip. di Matematica, Università degli Studi di Milano, Via C. Saldini, 50, 20133 Milano, Italy

  • Bruno Kahn

    IMJ-PRG, Case 247, 4 place Jussieu, 75252 Paris Cedex 05, France
A universal rigid abelian tensor category cover
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Abstract

We prove that any rigid additive symmetric monoidal category can be mapped to a rigid abelian symmetric monoidal category in a universal way. This sheds a new light on abelian -envelopes and on motivic conjectures such as Grothendieck's standard conjecture and Voevodsky's smash nilpotence conjecture.

Cite this article

Luca Barbieri-Viale, Bruno Kahn, A universal rigid abelian tensor category. Doc. Math. 27 (2022), pp. 699–717

DOI 10.4171/DM/882