Rendiconti del Seminario Matematico della Università di Padova

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Volume 139, 2018, pp. 205–224
DOI: 10.4171/RSMUP/139-8

Published online: 2018-06-06

Definable categories and $\mathbb T$-motives

Luca Barbieri-Viale[1] and Mike Prest[2]

(1) Università di Milano, Italy
(2) University of Manchester, UK

Making use of Freyd's free abelian category on a preadditive category we show that if $T\colon D\rightarrow \mathcal A$ is a representation of a quiver $D$ in an abelian category $\mathcal A$ then there is an abelian category $\mathcal A (T)$, a faithful exact functor $F_T\colon \mathcal A (T) \to \mathcal A$ and an induced representation $\widetilde T\colon D \to \mathcal A (T)$ such that $F_T\widetilde T= T$ universally. We then can show that $\mathbb T$-motives as well as Nori's motives are given by a certain category of functors on definable categories.

Keywords: Motives, model theory, representations, abelian categories

Barbieri-Viale Luca, Prest Mike: Definable categories and $\mathbb T$-motives. Rend. Sem. Mat. Univ. Padova 139 (2018), 205-224. doi: 10.4171/RSMUP/139-8