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@@ -113,7 +113,7 @@ Exercise: do those formally, as follows!
1. Prove that the homomorphism \\((f : A \to B) \mapsto (Gf)(a)\\) is indeed a homomorphism (that is, a natural transformation), by writing out the necessary properties which define a natural transformation and showing that they each hold. 1. Prove that the homomorphism \\((f : A \to B) \mapsto (Gf)(a)\\) is indeed a homomorphism (that is, a natural transformation), by writing out the necessary properties which define a natural transformation and showing that they each hold.
1. Prove (by writing out the equations) that the two Yoneda maps are inverse to each other. 1. Prove (by writing out the equations) that the two Yoneda maps are inverse to each other.
1. Write out the equations for both naturality conditions (that is, in \\(A\\) and in \\(F\\)) in full, and prove them. 1. Write out the equations for both naturality conditions (that is, in \\(A\\) and in \\(G\\)) in full, and prove them.
# The Yoneda embedding # The Yoneda embedding