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 D and Voevodsky's smash nilpotence conjecture.
A universal rigid abelian tensor category / L. BARBIERI VIALE, K. Bruno. - In: DOCUMENTA MATHEMATICA. - ISSN 1431-0643. - 27:(2022), pp. 699-717. [10.25537/dm.2022v27.699-717]
A universal rigid abelian tensor category
L. BARBIERI VIALE
Primo
;
2022
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 D and Voevodsky's smash nilpotence conjecture.
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