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    • CommentRowNumber1.
    • CommentAuthorTim Campion
    • CommentTimeFeb 14th 2021

    Added some basic examples from HTT. There doesn’t seem to be a page for the corresopnding 1-categorical notion. This notion is used pretty heavily in \infty-category theory, but it’s not so familiar from 1-category theory. But I’d have to think a 1-categorical treatment exists somewhere, right?

    diff, v2, current

    • CommentRowNumber2.
    • CommentAuthorAlexanderCampbell
    • CommentTimeFeb 15th 2021
    • (edited Feb 15th 2021)

    I know these from Schumacher & Street’s paper on Some parametrized categorical concepts as “cartesian cones”. Also, in the case of diagrams indexed by discrete categories, I think these are the “initial lifts” of “structured sources” from The Joy of Cats.

    • CommentRowNumber3.
    • CommentAuthorTim Campion
    • CommentTimeFeb 15th 2021
    • (edited Feb 15th 2021)

    Thanks! “Roughly equivalent” notions probably appear in different guises elsewhere too, of course.

    • CommentRowNumber4.
    • CommentAuthorTim Campion
    • CommentTimeFeb 27th 2021

    Added a better example which Rune Haugseng explained to me.

    diff, v3, current