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    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeApr 21st 2014

    Vladimir Sotirov has asked a question at contravariant functor.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeApr 21st 2014

    I’ve thought about considering categories with covariant and contravariant functors as forming a category enriched over Cat×CatCat\times Cat with a slightly funny non-symmetric monoidal structure, but that doesn’t allow for transformations that mix variance. Perhaps whoever wrote that page was thinking of a similar monoidal structure on Cat/ICat/I (with II the walking iso)?

    • CommentRowNumber3.
    • CommentAuthorZhen Lin
    • CommentTimeApr 21st 2014

    The underlying 1-category can be obtained as the Grothendieck construction applied to the obvious diagram of shape 𝔹(/2)\mathbb{B} (\mathbb{Z} / 2 \mathbb{Z}), but I don’t see how to get the 2-cells in a “natural” way.