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nLab > Latest Changes: hierarchy of universes

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  1. starting page on hierarchy of universes in type theory

    Anonymouse

    v1, current

  2. move section on cumulativity from type universe to hierarchy of universes

    Anonymouse

    v1, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 28th 2023

    Where you write “one could derive” you mean “one can derive”.

  4. replaced all instances of “could” with “can”

    Anonymouse

    v1, current

    • CommentRowNumber5.
    • CommentAuthorDean
    • CommentTimeApr 15th 2025
    • (edited Apr 16th 2025)
    I'm investigating the discrepancy between cocomplete elementary topoi with respect to a universe $\text{Type (u)}$ and a Grothendieck topos with respect to universe $\text{Type (v)}$.

    In the case where $\text{u = v = 1}$, this is usually fixed with the concept of a generating set, like here:

    topos#SheafToposes

    Also, in the case where $\text{u = v}$, a Grothendieck topos is a cocomplete elementary topos.

    Is there an operation on sorts $\text{S}$ such that, if we fix $\text{v = }\text{S}(\text{u})$, then a cocomplete elementary topos is a Grothendieck topos?
    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeApr 16th 2025

    Can you please fix your formatting and also not use fake cursive font?

    • CommentRowNumber7.
    • CommentAuthorDean
    • CommentTimeApr 16th 2025
    Sorry, but iTeX doesn't seem to be working even though I selected it that way in the box.

    I believe that the successor universe of +1 should be able to play the role of the sort operator.
    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2025
    • (edited Apr 16th 2025)

    Dean,

    no, iTex was and is working, as you can see by your \mathcal-command being rendered.

    But the command \texttt is not supported by iTex, as you can also see just by looking at the rendered output (click on “Preview Post” below the edit pane before submitting with the “Add your comments”-button right next to it).

    What is more, neither command is what you should actually want to use here.

    Just delete the “\text” and “\texttt” command and also the “\mathcal“-command, and then your comment will become readable .

    (You may not need to resubmit your comment, but may be able to edit the already posted comment, by clicking the button “edit” at the top right of the edit pane, if you have that button. Maybe not, I forget if this functionality is offered to all users.)

    • CommentRowNumber9.
    • CommentAuthorDean
    • CommentTimeApr 17th 2025
    • (edited Apr 18th 2025)
    Ok I see. In fixing it I figured out that Safari doesn't support iTex but it does support Math ML
    • CommentRowNumber10.
    • CommentAuthorDean
    • CommentTimeApr 17th 2025
    • (edited Apr 18th 2025)
    <form method="get" action="https://www.google.com/search">
    <div style="display: flex; align-items: center;">
    <button type="submit" style="
    padding: 4px 6px;
    background-color: #fffff0;
    border: none;
    border-radius: 4px;
    margin-right: 2px;
    cursor: pointer;">
    <img src="https://ncatlab.org/nlab/files/GLOGO.png"
    alt="nLab"
    style="height: 20px; vertical-align: middle;" />
    </button>
    <input
    type="text"
    name="q"
    value="site:ncatlab.org/nlab/ "
    style="padding: 6px;
    width: 200px;
    font-size: 14px;
    border: 2px solid #fffff0;
    border-radius: 4px;
    font-family: sans-serif;
    background: #fffff0;
    color: black;
    outline: none;"
    onfocus="this.style.borderColor='#3a53a4'"
    onblur="this.style.borderColor='#fffff0'" />
    </div>
    </form>

    Macro for nlab search:

    ```
    <form method="get" action="https://www.google.com/search">
    <div style="display: flex; align-items: center;">
    <button type="submit" style="
    padding: 4px 6px;
    background-color: #fffff0;
    border: none;
    border-radius: 4px;
    margin-right: 2px;
    cursor: pointer;">
    <img src="https://ncatlab.org/nlab/files/GLOGO.png"
    alt="nLab"
    style="height: 20px; vertical-align: middle;" />
    </button>
    <input
    type="text"
    name="q"
    value="site:ncatlab.org/nlab/ "
    style="padding: 6px;
    width: 200px;
    font-size: 14px;
    border: 2px solid #fffff0;
    border-radius: 4px;
    font-family: sans-serif;
    background: #fffff0;
    color: black;
    outline: none;"
    onfocus="this.style.borderColor='#3a53a4'"
    onblur="this.style.borderColor='#fffff0'" />
    </div>
    </form>
    ```
    • CommentRowNumber11.
    • CommentAuthorDean
    • CommentTimeApr 17th 2025
    • (edited Jul 25th 2025)
    [deleted]

  12. Coq -> Rocq

    type theorist

    diff, v9, current

1 to 12 of 12

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