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7 votes

Yoneda on a not so small category

You could use the usual device of assuming a Grothendieck universe: Mac Lane does this in [Categories for the working mathematician]. But actually you don't need that for the Yoneda lemma – you could …
Zhen Lin's user avatar
  • 15.9k
8 votes
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Unicity of Yoneda isomorphism

If there is an isomorphism $\mathrm{Hom}(y C, P) \cong P (C)$ natural in $P$ and $C$, then by restricting to the representable functors one obtains an automorphism of the identity functor of the categ …
Zhen Lin's user avatar
  • 15.9k