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Quiver: A Modern Commutative Diagram Editor

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Re: Quiver: A Modern Commutative Diagram Editor

#23
post #12
post #10

Earlier quoted context omitted.

It would help if you read the definition of a category. It is very abstract but also pretty simple with just a couple of axioms. An example of a category is the "sets and functions" category. In that category, every conceivable set lives as an object (node) and every conceivable function between any two sets lives as an arrow between these two sets. So, you can take an arrow from A to B and one from B to C and compos…

It would help if someone could tell what's wrong in my reply.

I didn't downvote you, but honestly, it doesn't really help understand what commuting diagrams are. I use them all the time, and never use category theory.

Your description was all abstraction, and I can't imagine would help anyone who didn't already know what we are talking about.

A concrete example would greatly help!

Re: Quiver: A Modern Commutative Diagram Editor

#26
post #9

This tool is fantastic! I was able to generate a Fourier-Poisson cube [0] in about 10 minutes, and the UI is incredibly intuitive. The focus on commutative diagrams, rather than a free-form canvas, is a brilliant design choice that keeps it clean and easy to use. I wish I'd had this during my thesis; it would have saved so much time. [0] https://q.uiver.app/#q=WzAsOCxbMCwxLCJnIFxcdGV4dHsgb24gfVxcb...

In case anyone else is curious about this, I found the reference to be Kammler's "A First Course in Fourier Analysis".

Re: Quiver: A Modern Commutative Diagram Editor

#28

Can anyone explain what "commutative and pasting diagrams" are to a humble (and not very good) software writer? The Wikipedia page was too abstract for me to understand at a basic level [0]. [0]: https://en.wikipedia.org/wiki/Commutative_diagram

They're just a nice way of writing equations between functions (or other things that compose like functions). This is a picture of a function f that takes inputs from A and produces outputs in B f A → B and this diagram f A → B ↘ ↓ g h C just means g ∘ f = h, ie. doing f then g is the same as doing h. Since you write the domain and codomain of each function, it makes it easier to see when the functions can compose (i…

> For example, associativity is inherent in the notation: A→B→C→D is the only way to express the composition of three functions, you can't even write the difference between (f∘g)∘h and f∘(g∘h).

It's only unwritable in a linear picture. If you wanted to make associativity visible, then you could express it in terms of commutativity using arrows that hop over nodes.

Re: Quiver: A Modern Commutative Diagram Editor

#29
post #7
post #4

Earlier quoted context omitted.

A commutative diagram is just a collection of nodes and directed edges between nodes (aka, a directed graph), but it's a directed graph along with the claim that any two paths in this graph which start at the same node and end at the same node are to be considered equivalent, in some sense. In general, a directed (multi)graph along with an account of which of its paths are and are not to be considered equivalent to e…

Note that Quiver isn't really a tool just for drawing "commutative diagrams". It's a tool for drawing any labeled system of nodes and edges/arrows between nodes, whether or not this is to be interpreted as a commutative diagram. (It also allows drawing arrows which start or end at other arrows, rather than at nodes). It has various features to control and adjust these diagrams to be visually pleasing, by changing siz…

> This is all much more convenient in its WYSIWYG interface than manually planning and coding these figures in LaTeX, as had previously been the standard way to create them for mathematical papers.

While I'm all for such convenience tools, I thought HN would be the place to find sympathy for the idea behind tikz-cd and its predecessors like xypic, that it's easier to write code that can be easily reproduced and programmatically manipulated than it is to try to draw (by hand, or with something like xfig), which was previously to that the standard. I guess preferences are cyclical!

Re: Quiver: A Modern Commutative Diagram Editor

#30
post #29
post #7

Earlier quoted context omitted.

Note that Quiver isn't really a tool just for drawing "commutative diagrams". It's a tool for drawing any labeled system of nodes and edges/arrows between nodes, whether or not this is to be interpreted as a commutative diagram. (It also allows drawing arrows which start or end at other arrows, rather than at nodes). It has various features to control and adjust these diagrams to be visually pleasing, by changing siz…

> This is all much more convenient in its WYSIWYG interface than manually planning and coding these figures in LaTeX, as had previously been the standard way to create them for mathematical papers. While I'm all for such convenience tools, I thought HN would be the place to find sympathy for the idea behind tikz-cd and its predecessors like xypic, that it's easier to write code that can be easily reproduced and progr…

Quiver exports to tikz-cd for what it’s worth. Not sure how readable the code tends to be though
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