A universal rigid abelian tensor category

@inproceedings{BarbieriViale2021AUR,
  title={A universal rigid abelian tensor category},
  author={Luca Barbieri-Viale and Bruno Kahn},
  year={2021}
}
We prove that any rigid additive symmetric monoidal category can be mapped to a rigid abelian symmetric monoidal category in a universal way. This yields a novel approach to Grothendieck’s standard conjecture D and Voevodsky’s smash nilpotence conjecture. 

References

SHOWING 1-10 OF 49 REFERENCES
Universal rigid abelian tensor categories and Schur finiteness
We study the construction of [4] in more detail, especially in the case of Schur-finite rigid ⊗-categories. This leads to some groundwork on the ideal structure of rigid additive and abelian
Monoidal abelian envelopes
We prove a constructive existence theorem for abelian envelopes of non-abelian monoidal categories. This establishes a new tool for the construction of tensor categories. As an example we obtain new
Tensor structure for Nori motives
We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative
Algebraic cycles on an abelian variety
Abstract It is shown that to every ℚ-linear cycle ᾱ modulo numerical equivalence on an abelian variety A there is canonically associated a ℚ-linear cycle α modulo rational equivalence on A lying
Exactness and faithfulness of monoidal functors
Inspired by recent work of Peter O’Sullivan, we give a condition under which a faithful monoidal functor between abelian ⊗-categories is exact.
Representations in Abelian Categories
Consider the general but imprecise question: given a category how nicely can it be represented in an abelian category?
Motives , numerical equivalence , and semi-simplicity
In this note we show that the category of motives, as defined via algebraic correspondences modulo an adequate equivalence relation, is a semi-simple abelian category i f and in fact, only i f the
Autonomization of Monoidal Categories
TLDR
It is shown that contrary to common belief in the DisCoCat community, a monoidal category is all that is needed to define a categorical compositional model of natural language, and the applications of this principle to various distributional models of meaning are illustrated.
A nilpotence theorem for cycles algebraically equivalent to zero
In this paper we prove that a correspondence from a smooth projective variety over a field to itself which is algebraically equivalent to zero is a nilpotent in the ring of correspondences modulo
Definable Additive Categories: Purity and Model Theory
Definable additive categories and their model theory are the topic of this paper. We begin with background and preliminary results on additive categories. Then definable subcategories, their
...
...