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I made some minor improvements to the Properties section of pushout, making it match the similar section in pullback insofar as it can. (It’s a bit tiring to have to look at both these pages to get all the basic properties, so I fixed that, but for properties that hold both for pullbacks and dually for pushouts I’m happy to have all the proofs at pullback - that’s how it works now.)
Thanks!
You don’t need to propose changes before doing them. In fact, experience shows that changes that are being proposed here tend to never be implemented.
The modus operandi is that if you are energetic about making a certain edit, then you are likely the single best person to make that edit at that point in time. Moreover, an actual edit tends to get much more and more useful feedback than the proposal of an edit. And in case that a real objection to an edit should arise, it is still easy to adjust (or, in rare cases, revert) afterwards.
So please go ahead.
What is it about the coequalizer diagram that you have in mind?
You can adjust length of arrows in tikzcd
either globally or individually.
In the present case, I have adjusted here the right arrow by adding [-35pt]
after its ampersand
\begin{tikzcd}
a
\ar[r, "i_1 \circ f", shift left]
\ar[r, "i_2 \circ g"', shift right]
&
b \sqcup c
\arrow[r]
&[-35pt]
b
\underset{a}{\sqcup}
c
\end{tikzcd}
(To shrink arrows globally, add something like [column sep=30pt]
after \begin{tikzcd}
. But if one does this then, currently on the $n$Lab, also the font size of the entire diagram shrinks, for some reason. So maybe better to adjust locally.)
While I was at it, I also took the liberty of replacing subscripted additive notation for cofiber coproducts by more coproduct-like notation.
I am deleting all redirects for amalgam*
that were pointing to here, and instead will create now a disambiguation entry amalgamation
this since common usage of terminology is such that most readers looking for “amalgamation” are probably really after amalgamated free products of groups as (now) described at free product of groups and if we do want to make the point that this is a special case of a pushout then we should do so up front in a dedicated disambiguation entry
[edit: in making this edit I am being alerted that the previous redirects had been clashing with the entry amalgamation property all along, so one more reason to have them removed, as they are now]
added pointer to:
added pointer to:
for the terminology “amalgamated sum”.
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