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Where you write “one could derive” you mean “one can derive”.
I’m investigating the discrepancy between cocomplete elementary topoi with respect to a universe Type (u) and a Grothendieck topos with respect to universe Type (v).
In the case where u = v = 1, this is usually fixed with the concept of a generating set, like here:
Also, in the case where u = v, a Grothendieck topos is a cocomplete elementary topos.
Is there an operation on sorts S such that, if we fix v =S(u), then a cocomplete elementary topos is a Grothendieck topos?
Can you please fix your formatting and also not use fake cursive font?
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.
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.)
Ok I see. In fixing it I figured out that Safari doesn’t support iTex but it does support Math ML
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>
It looks like you can do some neat things with Math ML. Above I made an example of a search box.
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