What is the enriched Yoneda lemma?

Conditions

• The setting is enriched category theory.
• Hom_X denotes the representable functor at X.
• F is a functor in the same enriched context.

Reasoning, step by step

1. Identify the enriched category context.
2. Consider the enriched natural transformations from Hom_X to F.
3. Conclude that this object is isomorphic to $F(X)$ in the enriching category.

Example

The speaker states: 'the set of enriched natural transformations from Hom X to F is isomorphic as an object, e.g. a topological space, to F of X.'

Common misconceptions

• Thinking the enriched Yoneda lemma only applies to sets.
• Assuming the isomorphism is always a set-theoretic bijection.

Watch the explanation

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