corollary. evaluation functor preserves limits of ... [leinster2016basic, 6.2.6] [tt-0046]

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An important corollary of theorem [tt-0045].

The Yoneda embedding preserves limits, for any small category [leinster2016basic, 6.2.12]. But it does not preserve colimits in general [leinster2016basic, 6.2.14].

Every presheaf can be expressed as a colimit of representables in a canonical (though not unique) way, this is theorem [tt-004D], and dual to lemma [tt-002N].