nLab Yoneda lemma - contents

Yoneda lemma

Ingredients

• category

• functor

• natural transformation

• presheaf

• category of presheaves

• representable presheaf

• Yoneda embedding

Incarnations

• Yoneda lemma

• enriched Yoneda lemma

• co-Yoneda lemma

• Yoneda reduction

Properties

• free cocompletion

• Yoneda extension

Universal aspects

• representable functor

• universal construction

• universal element

Classification

• classifying space, classifying stack

• moduli space, moduli stack, derived moduli space

• classifying topos

• subobject classifier

• universal principal bundle, universal principal ∞-bundle

• classifying morphism

Induced theorems

• Tannaka duality

…

In higher category theory

Yoneda lemma for higher categories:

• Yoneda lemma for (∞,1)-categories

• Yoneda lemma for bicategories

• Yoneda lemma for tricategories

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