Definition of Yoneda embedding

1. Noun. (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] . ¹



¹ Source: wiktionary.com

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Lexicographical Neighbors of Yoneda Embedding

Yogi Berra
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Yolngu
Yom Kippur
Yom Kippur War
Yomi
Yoneda embedding (current term)
Yoneda lemma
Yonkers
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Yonner
Yonners
York
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York ham
Yorke
Yorke's autolytic reaction
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Yorks
Yorkshire

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