Re: Fundamental Theorem of Category Theory?

[Vaughan Pratt <pratt@cs.stanford.edu>]

Apropos of the Yoneda Lemma, is there some reason why it is usually
stated on its own rather than as one direction of a characterization of
categories of presheaves on J?  Unless I've overlooked or misunderstood
something it seems to me that the Yoneda Lemma should state that C is a
category of presheaves on J if and only if there exists a full,
faithful, and dense functor from J to C.

This should generalize the characterization of an Archimedean field as
any dense extension of the rationals.

Vaughan Pratt


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