Math 762 Spring 2016 Homework 3 Drew Armstrong
نویسنده
چکیده
The Yoneda Lemma tells us that the Hom bifunctor is “non-degenerate” in a similar way. (a) For each object X ∈ C verify that hX := HomC(X,−) defines a functor C → Set. (b) Given two objects X,Y ∈ C state what it means to have hX ≈ hY as functors. (c) Given two objects X,Y ∈ C and an isomorphism of functors hX ≈ hY , prove that we have an isomorphism of objects X ≈ Y . [Hint: Let Φ : hX ∼ −→ hY be a natural isomorphism. Now consider the morphisms ΦX(idX) : Y → X and (ΦY )(idY ) : X → Y .]
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