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    • CommentRowNumber1.
    • CommentAuthorTobyBartels
    • CommentTimeApr 27th 2011

    I’ve disambiguated links to cartesian category. I suggest that we avoid this term.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 27th 2011

    Thanks. Okay, so I am in 2:1 minority about this.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeApr 28th 2011

    The problem with “cartesian” for “finitely complete” is that it is also used to refer only to finite products, as for instance in cartesian bicategory and cartesian object. I find it ironic that elsewhere in the Elephant, Johnstone declines to use the absolutely standard word “cartesian” for cartesian morphisms on the grounds that the word “cartesian” has been “rather overworked by category-theorists” – but he does choose to use “cartesian” for “finitely complete”, where it is not standard at all. I think “finitely complete” has the advantage of being completely unambiguous. If it seems too long, then one can also just say “lex”, which is also completely unambiguous, but may require explanation to people who haven’t heard it before.

    • CommentRowNumber4.
    • CommentAuthorSridharRamesh
    • CommentTimeMay 6th 2011
    • (edited May 6th 2011)
    And of course, there is the perhaps most familiar use of cartesian with the requirement only of finite products rather than all finite limits: "cartesian closed category".

    Anyway, I also dislike the term "cartesian category" for the same reasons, whatever weight that unsolicited opinion carries.