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nLab > Latest Changes: Closed Category, Category of V-enriched Categories

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  1. I have edited the articles on closed category and unit enriched category with a view toward a substantial revision of category of V-enriched categories. My primary purpose will be to document the extra structure necessary to realize a $2$-category as a $2$-category of $V$-enriched categories for the various contexts (at least for the monoidal and closed contexts anyway). In particular, I hope to motivate the structure of a closed category $C$ as the minimal amount of structure necessary to recover a $2$-category of categories enriched in self-enriched $C$.
    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeApr 15th 2014

    I hope to motivate the structure of a closed category CC as the minimal amount of structure necessary to recover a 22-category of categories enriched in self-enriched CC.

    That sounds interesting!

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeApr 15th 2014

    This is interesting, but I wonder whether it’s appropriate for the “Idea” section of closed category, since it seems a bit esoteric. Maybe we could put it a bit further down the page?

  4. I have added some material in contravariant functor which I need for the closed category stuff. I think I have done something wrong when trying to make my last commutative diagram, as it displays both the source code and the rendered diagram, messing up the formatting. Any assistance (and references for this stuff!) would be much appreciated as I'm mostly flying by the seat of my pants here.
    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeApr 18th 2014

    Since no one replied to #3, and in particular no one objected, I’ve moved the material in question further down the page of closed category into a subsection of “Properties”.

  6. Thank you, Mike. I have edited further (for clarity) my addition to closed category, and have also further developed my addition to category of V-enriched categories (which depends on my addition to contravariant functor). I apologize for formatting or structural issues I may have introduced to those articles, and I hope the new content makes up for them. My edits are still in flux, slowly shaping up, but I think by this point I have added enough to make evident the gist of the construction I'm trying to do. Any comments and opinions will be much appreciated.

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