stylistic:style_transfer, structural:reformatting, linguistic:paraphrasing, quality:correction
Representable functor

The Yoneda embedding essentially states that for every (locally small) category, objects in that category can be represented by presheaves, in a full and faithful manner. That is,

for a presheaf P. Many common categories are, in fact, categories of pre-sheaves, and on closer inspection, prove to be categories of sheaves, and as such examples are commonly topological in nature, they can be seen to be topoi in general. The Yoneda lemma provides a point of leverage by which the topological structure of a category can be studied and understood.