Category of presheaves

The category of presheaves $𝖯 𝖲 𝗁 (𝖢) : = 𝖲 𝖾 𝗍 𝖢 𝐨 𝐩$ is a category where an object is a Presheaf and a morphism is a natural transformation. #m/def/cat Thus it is a particular example of a functor category.

Properties

By the Yoneda embedding, $𝖢$ is a full subcategory of $𝖯 𝖲 𝗁 (𝖢)$ .

Examples

Many categories of interest are conveniently expressed as the presheaves of a “presenting category.”

$𝖰 𝗎 𝗂 𝗏$
Category of simplicial sets

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