Definable categories and $\mathbb T$-motives
| Autor: | Mike Prest, Luca Barbieri-Viale |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Model theory
Pure mathematics Algebra and Number Theory Functor Preadditive category Induced representation 010102 general mathematics Quiver Representation (systemics) 16. Peace & justice 01 natural sciences Mathematics::Category Theory 0103 physical sciences 010307 mathematical physics Geometry and Topology Abelian category 0101 mathematics Exact functor Mathematical Physics Analysis Mathematics |
| Zdroj: | Rendiconti del Seminario Matematico della Università di Padova. 139:205-224 |
| ISSN: | 0041-8994 |
| DOI: | 10.4171/rsmup/139-8 |
| Popis: | Making use of Freyd's free abelian category on a preadditive category we show that if $T:D\rightarrow \mathcal{A}$ 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 $F_T: \mathcal{A} (T) \to \mathcal{A}$ and an induced representation $\tilde T: D \to \mathcal{A} (T)$ such that $F_T\tilde T= T$ 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. |
| Databáze: | OpenAIRE |
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