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nLab > Latest Changes: created limit

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 21st 2021
    • (edited Apr 21st 2021)

    Where the example of monadic functors creating limits is mentioned, there should be a reference, at least.

    I have added pointer to MacLane 71, Exercise IV.2.2 (p. 138)

    Scanning through Borceux II, I don’t spot the statement there. (?)

    diff, v13, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 11th 2022
    • (edited Aug 11th 2022)

    added pointer to:

    here, and in related entries

    diff, v16, current

  3. Added the remark that for amnestic isofibrations the strict and the non-strict notion of creation of limits are equivalent.

    Jonas Frey

    diff, v17, current

    • CommentRowNumber4.
    • CommentAuthorjonsterling
    • CommentTimeFeb 12th 2023
    Unless I am confused, my copy of Mac Lane does not in fact require limits that don't exist in the codomain to be created. Mac Lane says:

    > A functor V : A -> X creates limits for a functor F : J -> A if:
    > (i) to every limiting cone \tau : x -> VF in X there is exactly one ......

    So the limiting cone is assumed to exist in the codomain category. So what is going on in this nlab page? Did I misunderstand the discussion?
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeFeb 12th 2023

    You are probably referring to the subsection here.

    This was added by Mike in revision 11, Feb 2018.

    Interesting to compare to the status of revision 10. Don’t know what happened there.

    • CommentRowNumber6.
    • CommentAuthorvarkor
    • CommentTimeApr 11th 2023

    Mention terminology “closed under limits”.

    diff, v19, current

    • CommentRowNumber7.
    • CommentAuthorʇɐ
    • CommentTimeJan 29th 2024

    The stated definition for creation of limits (namely that the functor preserves and reflects limits) doesn’t match that of any of the three references; they all add the requirement that the functor F:C→D F \colon C \to D also lifts limit cones, i.e. if every limit cone in the codomain over F∘J F \circ J is the image along F F of some limit cone over J J (following Riehl) or of a unique cone over J J and this cone is limiting (Mac Lane and Adámek–Herrlich–Strecker). Is there any reference for the term as used on this page, or is it a mistake?

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 30th 2024
    • (edited Jan 30th 2024)

    As mentioned in #5 above,

    the entry used to say this until revision 10,

    it was changed by Mike in revision 11, Feb 2018.

    • CommentRowNumber9.
    • CommentAuthorʇɐ
    • CommentTimeJan 30th 2024

    Whoops, missed that completely! 😅 Looking at it again I now see that the existence of a lifting (up to isomorphism this time) is also part of this definition: J J is required to have a limit, and preservation and reflection do the rest. (Maybe the strict variant and the differences should be mentioned earlier up on the page, for undercaffeinated readers…)

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJan 30th 2024

    I think the entry deserves clarification, given that it keeps tripping up people.

    The traditional definition from revision 10 should not remain deleted but be re-instantiated, and then referred to for comparison.

    I don’t have the energy now to edit this entry, but if anyone has, it would be welcome.

1 to 10 of 10

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