Definable categories and T-motives

Luca Barbieri-Viale; Michael Prest

doi:10.4171/RSMUP/139-8

Definable categories and T-motives

Luca Barbieri-Viale, Michael Prest

Universita Degli Studi di Milano

Research output: Contribution to journal › Article › peer-review

Abstract

Making use of Freyd's free abelian category on a preadditive category we show that if T:D→A is a representation of a quiver D in an abelian category A then there is an abelian category A(T), a faithful exact functor FT:A(T)→A and an induced representation T~:D→A(T) such that FTT~=T universally. We then can show that T-motives as well as Nori's motives are given by a certain category of functors on definable categories.

Original language	English
Journal	Rendiconti del Seminario Matematico della Università di Padova
Volume	139
Early online date	6 Jun 2018
DOIs	https://doi.org/10.4171/RSMUP/139-8
Publication status	Published - 2018

Access to Document

10.4171/RSMUP/139-8

https://arxiv.org/abs/1604.00153

Cite this

@article{3e6f7c4d83ab48e4b8bfd14df2c8ee3e,

title = "Definable categories and T-motives",

abstract = "Making use of Freyd's free abelian category on a preadditive category we show that if T:D→A is a representation of a quiver D in an abelian category A then there is an abelian category A(T), a faithful exact functor FT:A(T)→A and an induced representation T~:D→A(T) such that FTT~=T universally. We then can show that T-motives as well as Nori's motives are given by a certain category of functors on definable categories. ",

author = "Luca Barbieri-Viale and Michael Prest",

year = "2018",

doi = "10.4171/RSMUP/139-8",

language = "English",

volume = "139",

journal = "Rendiconti del Seminario Matematico della Universit{\`a} di Padova",

issn = "0041-8994",

publisher = "European Mathematical Society Publishing House",

}

TY - JOUR

T1 - Definable categories and T-motives

AU - Barbieri-Viale, Luca

AU - Prest, Michael

PY - 2018

Y1 - 2018

N2 - Making use of Freyd's free abelian category on a preadditive category we show that if T:D→A is a representation of a quiver D in an abelian category A then there is an abelian category A(T), a faithful exact functor FT:A(T)→A and an induced representation T~:D→A(T) such that FTT~=T universally. We then can show that T-motives as well as Nori's motives are given by a certain category of functors on definable categories.

AB - Making use of Freyd's free abelian category on a preadditive category we show that if T:D→A is a representation of a quiver D in an abelian category A then there is an abelian category A(T), a faithful exact functor FT:A(T)→A and an induced representation T~:D→A(T) such that FTT~=T universally. We then can show that T-motives as well as Nori's motives are given by a certain category of functors on definable categories.

U2 - 10.4171/RSMUP/139-8

DO - 10.4171/RSMUP/139-8

M3 - Article

SN - 0041-8994

VL - 139

JO - Rendiconti del Seminario Matematico della Università di Padova

JF - Rendiconti del Seminario Matematico della Università di Padova

ER -

Definable categories and T-motives

Abstract

Access to Document

Fingerprint

Cite this