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    • CommentRowNumber1.
    • CommentAuthorvarkor
    • CommentTimeFeb 21st 2024

    Mention terminology “preterminal object”.

    diff, v18, current

    • CommentRowNumber2.
    • CommentAuthorHurkyl
    • CommentTimeFeb 22nd 2024

    Changed the wording of an equivalent statement, so that it doesn’t leave open the possibility of a subterminal object UU for which U×UU \times U doesn’t exist.

    diff, v19, current

    • CommentRowNumber3.
    • CommentAuthormaxsnew
    • CommentTimeFeb 22nd 2024

    Why not just say that the cone UUUU \leftarrow U \rightarrow U given by identities is a product?

    • CommentRowNumber4.
    • CommentAuthorHurkyl
    • CommentTimeFeb 22nd 2024
    • (edited Feb 22nd 2024)

    I was just making an (IMO) minimal adjustment to the existing language. I don’t really know what precisely the original wording wanted to emphasize. I just wanted to reword it to forestall any reactions wondering about U×UU \times U not existing that might slow a reader down.

    • CommentRowNumber5.
    • CommentAuthormaxsnew
    • CommentTimeFeb 22nd 2024

    Another rewording of the product condition

    diff, v20, current

    • CommentRowNumber6.
    • CommentAuthorRodMcGuire
    • CommentTimeFeb 22nd 2024


    An object UU in a category CC is subterminal or preterminal if any two morphisms with target UU and the same source are equal. In other words, UU is subterminal if for any object XX, there is at most one morphism XUX\to U.

    If C has a terminal object 1, then U is subterminal precisely if the unique morphism U→1 is monic, so that U represents a subobject of 1; hence the name “sub-terminal.”

    like anything associated with limits while the objects are unique the morphisms from or to them are not equal or unique but only unique up to isomorphism,

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeFeb 22nd 2024
    • (edited Feb 22nd 2024)

    Re #6: The quoted text looks correct. The sentence after the quote seems to have the roles of objects and morphisms mixed up.