In detail, a functor F:CD is representably fully faithful on cores if it satisfies the conditions in Remark 9.8.4.1.2 and Remark 9.8.5.1.2, i.e.:

  1. 1. For all diagrams of the form

    with α and β natural isomorphisms, if we have idFα=idFβ, then α=β.

  2. 2. For each XObj(Cats) and each natural isomorphism
    of C, there exists a natural isomorphism
    of C such that we have an equality
    of pasting diagrams in Cats2, i.e. such that we have
    β=idFα.


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