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fix one other subscript
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mikeshulman committed Sep 3, 2015
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Expand Up @@ -952,7 +952,7 @@ \section{The Yoneda lemma}
This gives a function $(\alpha \mapsto \alpha_a(1_a))$ from left to right in~\eqref{eq:yoneda}.

In the other direction, given $x:F a$, we define $\alpha:\y a \to F$ by
\[\alpha_{a'}(f) \defeq F_{a',a}(f)(x). \]
\[\alpha_{a'}(f) \defeq F_{a,a'}(f)(x). \]
Naturality is easy to check, so this gives a function from right to left in~\eqref{eq:yoneda}.

To show that these are inverses, first suppose given $x:F a$.
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