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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 2nd 2012

    I have finally split off dependent sum from dependent product. And added a few more paragraphs.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 4th 2014

    Added a section Relation to some limits with the remarks that dependent sum to the points preserves fiber products and that the naturality squares of the unit are pullbacks.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 5th 2017

    Is that a little confusing at dependent sum to have it be left adjoint to base change for any f:AIf:A \to I, then later consider only terminal maps?

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 7th 2018

    Returning to my comment in #3, do type theorists use the terms dependent sum (or pair) and dependent product for adjoints to base change for general f:ABf: A \to B, or only for terminal maps?

    Does anyone know the history of this? When did Martin-Löf first talk about dependent sum/product? Would he use the terms in the more general sense?

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeJun 7th 2018

    I don’t know the history. In general, dependent sum/product are used in type theory for syntax that corresponds to adjoints to base change along a display map (i.e. to a map with terminal codomain, but in an arbitrary context). But since every map is isomorphic (in extensional type theory) or equivalent (in homotopy type theory) to a display map, in category theory we tend to use the words for adjoints to base change along an arbitrary map.

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