Implications of Yoneda Lemma to Category Theory
نویسندگان
چکیده
This is a survey paper on the implication of Yoneda lemma, named after Japanese mathematician Nobuo Yoneda, to category theory. We prove Yoneda lemma. We use Yoneda lemma to prove that each of the notions universal morphism, universal element, and representable functor subsumes the other two. We prove that a category is anti-equivalent to the category of its representable functors as a corollary of Yoneda lemma. We also prove the Yoneda embedding, i.e. representable functors are isomorphic if and only if their representers are isomorphic.
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