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    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 27th 2012

    I pasted in something Mike wrote on sketches and accessible models to sketch. But now it needs tidying up, and I’m wondering if it might have been better placed at accessible category. Alternatively we start a new page on sketch-theoretic model theory. Ideas?

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeSep 27th 2012

    Putting it at accessible category sounds good to me.

    • CommentRowNumber3.
    • CommentAuthorDexter Chua
    • CommentTimeAug 29th 2016

    Added a small idea section and an example.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeNov 10th 2017

    Andrée Ehresmann pointed out on the catlist that our definition of sketch was actually the definition of a realized sketch, so I fixed our page to the more general version.

  1. The category of sketches has a well behaved symmetric monoidal structure that can be useful when discussing models of theories inside of models of theories, such as double categories or vector bundle groupoids. I thought it might be useful to have on the nlab page for sketches.

    Ben MacAdam

    diff, v18, current

  2. Was intending just to do a little tidying and book-keeping, but ended up rewriting the idea section as well, and giving, for my sins, the full details of a couple of examples; writing down the full details of a sketch in practise is a little more subtle than one might think if one has not tried it.

    diff, v21, current

    • CommentRowNumber7.
    • CommentAuthorTim_Porter
    • CommentTimeAug 9th 2020

    Fixed an insecure link, replacing it by a Numdam link.

    diff, v23, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMar 21st 2021

    added pointer to:

    diff, v24, current

  3. In the previous version it was claimed that the tensor product of sketches was part of a symmetric monoidal structure on the category of sketches. That is wrong. I sketched the right statement (factors in the tensor product can be swapped if the specified limits and colimits commute), gave a reference, and gave an example (I think) where one can not switch the factors.

    Peter Arndt

    diff, v28, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeAug 24th 2021

    added pointer to the recent:

    diff, v29, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeAug 24th 2021

    added pointer to:

    diff, v30, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJun 4th 2022

    Fixed the first sentence from:

    A sketch is one formalisation of the notion of a theory


    The notion of a sketch is one formalisation of the notion of a theory

    diff, v31, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeMay 3rd 2023

    added pointer to:

    diff, v33, current

    • CommentRowNumber14.
    • CommentAuthorvarkor
    • CommentTimeOct 16th 2023

    Added a reference to a formal generalisation of the notion of sketch.

    diff, v34, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeNov 2nd 2023

    Where the entry claims that categories of models of limits sketches are the locally presentable categories (here) I added a pointer to a reference.

    diff, v38, current

    • CommentRowNumber16.
    • CommentAuthorvarkor
    • CommentTimeNov 30th 2023

    Added the original reference. Unfortunately, I can’t find a copy, so would be grateful if someone could upload it.

    diff, v40, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeNov 30th 2023
    • (edited Nov 30th 2023)

    The article is contained in his Oeuvres complètes et commentées, on pp. 39 here.

    I have uploaded a small pdf, here.

    • CommentRowNumber18.
    • CommentAuthorvarkor
    • CommentTimeNov 30th 2023

    Thanks, I had accidentally been looking in IV.2 rather than IV.1, which is why I missed it.