Definable categories and 𝕋-motives
Barbieri-Viale, Luca1 ; Prest, Mike2
1 Università di Milano, Italy
2 University of Manchester, UK
Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 205-224.

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 F T :𝒜(T)→𝒜 and an induced representation T ˜:D→𝒜(T) such that F T T ˜=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.

Publié le :
DOI : 10.4171/RSMUP/139-8
Classification : 14, 03, 18, 19
Mots clés : Motives, model theory, representations, abelian categories
Barbieri-Viale, Luca 1 ; Prest, Mike 2

1 Università di Milano, Italy
2 University of Manchester, UK 
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     title = {Definable categories and $\mathbb T$-motives},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
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Barbieri-Viale, Luca; Prest, Mike. Definable categories and $\mathbb T$-motives. Rendiconti del Seminario Matematico della Università di Padova, Tome 139 (2018), pp. 205-224. doi : 10.4171/RSMUP/139-8. http://www.numdam.org/articles/10.4171/RSMUP/139-8/

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