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    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 8th 2019

    Added a reference

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 14th 2020

    Does anything prevent a codensity monad construction for the inclusion of FinCat into Cat?

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 14th 2020

    Mike’s asking about the inclusion of finitely presented (\mathcal{X}_i, \mathcal{O}_{\mathcal{X_\infty-groupoids, back here. Does changing ’finite’ to ’finitely presented’ make a difference to my question?

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 14th 2020

    I guess there’s also the inclusion of finite sets into CatCat as discrete categories. That might be nearer ultracategories.

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 16th 2020

    Added a reference

    diff, v5, current

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 23rd 2020

    I was thinking ultracategories should be a kind of generalized multicategory, and it seems they (or least some form of them) are.

    I don’t know why they say

    we introduce a new structure called ultracategory which simultaneously generalizes the notions of topological space and of category

    when Makkai had already coined the term. Seeing that Lurie’s notion is slightly different from the latter’s, there’s then the question of where this third notion fits.

    diff, v7, current

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 23rd 2020

    Added a little more detail. Also that the Clementino-Tholen concept is different.

    diff, v8, current

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