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nLab > Latest Changes: functor comprehension principle

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  1. copied article from the michaelshulman wiki at functor comprehension principle (michaelshulman) to the nlab wiki.

    C. Silva

    v1, current

    • CommentRowNumber2.
    • CommentAuthormaxsnew
    • CommentTimeJun 17th 2023

    Is there a syntactic description somewhere of what the internal language of a regular category is?

    • CommentRowNumber3.
    • CommentAuthormaxsnew
    • CommentTimeJun 17th 2023

    Looks like it’s (somewhat sketchily) described here: https://ncatlab.org/michaelshulman/show/internal+logic+of+a+2-category#fragments_of_logic

    • CommentRowNumber4.
    • CommentAuthorvarkor
    • CommentTimeJun 17th 2023

    @maxsnew: have you seen Butz’s Regular Categories and Regular Logic?

    • CommentRowNumber5.
    • CommentAuthormaxsnew
    • CommentTimeJun 17th 2023

    Sorry, typo, I meant a regular 2-category which is what is used in the linked article.

    • CommentRowNumber6.
    • CommentAuthormaxsnew
    • CommentTimeFeb 27th 2024

    Add an idea section, relating it more directly to the function comprehension principle and also include another principle that I think is clearly deserving of the name “functor comprehension”. This page should also eventually get merged with representability determines functoriality.

    diff, v2, current

    • CommentRowNumber7.
    • CommentAuthormaxsnew
    • CommentTimeFeb 27th 2024

    Also found some material on the anafunctor page that could be moved here: https://ncatlab.org/nlab/show/anafunctor#anafunctors_versus_representable_profunctors

    • CommentRowNumber8.
    • CommentAuthormaxsnew
    • CommentTimeNov 4th 2024

    brief explanation for why representable profunctors define functors, using full-faithfulness of the Yoneda embedding.

    diff, v4, current

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