Yoneda embedding (suomeksi)

Määritelmät:

(lb, en, category theory) Given category $\mathcal{C}$ , a '''Yoneda embedding''' for this category is a functor $\phi$ such that for any object ''A'' in $\mathcal{C}$ , $\phi: A \mapsto h^A$ and for any morphism $f:B \rightarrow A$ in $\mathcal{C}$ , $\phi: f \mapsto \eta: h^A \rightarrow h^B$ where the natural transformation ''η'' has components $\eta_X: s \mapsto s\circ f$ . Then $\phi: \mathcal{C}^{op} \rightarrow [\mathcal{C},\mathcal{S}ets]$ . Otherwise, it is a functor $\phi$ such that $\phi: A \mapsto h_A$ and for any $f:A \rightarrow B$ in $\mathcal{C}$ , $\phi: f \mapsto \eta: h_A \rightarrow h_B$ where ''η'' has components $\eta_X: s \mapsto f\circ s$ . Then $\phi: \mathcal{C} \rightarrow [\mathcal{C}^{op}, \mathcal{S}ets]$ .