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prose: prose pass on comma
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TOTBWF committed Feb 5, 2025
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Expand Up @@ -103,11 +103,11 @@ Comma categories are [[discrete two-sided fibrations]].
Comma-is-discrete-two-sided-fibration .factors _ = prop!
```

Every $B$-vertical morphism in a discrete two-sided fibration is [[cartesian|cartesian-morphism]],
but this is not neccesarily true of *every* morphism. For instance, cartesian
maps in comma categories are precisely squares that satisfy the following
pasting property: for every (potentially non-commuting) square of the below
form, if the outer square commutes, then the upper square commutes.
Every *$B$-vertical* morphism in a discrete two-sided fibration is [[cartesian|cartesian morphism]],
but this is not neccesarily true of *every* morphism. In our setting,
the cartesian maps are given by squares that satisfy the following
pasting property: for every (potentially non-commutative) square of the below
form, if the overall rectangle commutes, then the upper square commutes.

~~~{.quiver}
\begin{tikzcd}
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