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    • CommentRowNumber1.
    • CommentAuthorYuxi Liu
    • CommentTimeJul 5th 2020

    created the page

    v1, current

    • CommentRowNumber2.
    • CommentAuthorYuxi Liu
    • CommentTimeJul 5th 2020

    also I hope someone would check this since I’m not sure if it’s right

    v1, current

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 5th 2020

    Added related entries Adj and walking equivalence.

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 5th 2020

    Corrections/clarification of notation, removed the adjective ’freely’ from the description of the 2-arrows being generated by ι 0\iota_0 and ι 1\iota_1.

    diff, v2, current

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 5th 2020
    • (edited Jul 5th 2020)

    I think we should also describe the relation to Adj, namely the existence of a 2-functor Adj𝒜ℰAdj \to \mathcal{AE} that is a bijection on objects and inverts the 2-arrows (modulo checking these details). Maybe this is universal among all such 2-functors. There’s probably some nice computad way of saying this.

    • CommentRowNumber6.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 5th 2020
    • (edited Jul 5th 2020)

    Why is Proposition 3.1 stated in such a weak form (a mere existence statement)?

    Can we not upgrade it to an existence and uniqueness statement?

    Isn’t it true that functors AE→C are precisely adjoint equivalences? (Where an adjoint equivalence is equipped with a choice of units and counits.)

    • CommentRowNumber7.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 5th 2020

    I think the entry was largely cut and paste from walking equivalence and tweaked to be about adjoint equivalences. That’s why #2 asks for extra eyes on it.