What do k-cells represent in a quiver javascript object ?

[tjbcg]

I'm working on typst export of diagrams. Reading the code and the comments, I'm not entirely sure I understand what a k-cell conceptually is. Are 1-cells arrows, and 2-cells natural transformations ? Or are some (simple) arrows higher level sometimes ?

[varkor]

Yes, that's right. A 0-cell is a vertex/object, a 1-cell is an edge whose level is 1, a 2-cell is an edge whose level is 2, and so on.

The only subtlety is that each edge actually has two levels: the "actual" level is calculated as one more than the maximum of the source level and the target level, for instance, in the following:

quiver/src/ui.mjs

Line 7479 in 4fee690

super(ui.quiver, Math.max(source.level, target.level) + 1, label, label_colour);

This is used to sort edges by those they depend on, e.g. when exporting to LaTeX (so that objects are exported first, then edges between objects, then edges between edges between objects, and so on). The other is the "visual" level, which corresponds to the "Level" slider in the quiver UI: this is how the edge is rendered, e.g. as a single arrow, double arrow, and so on. By default, the visual level is set to the actual level, but the user can override that.

In the LaTeX export, for instance, you can see the actual level being used to sort the edges:

quiver/src/quiver.mjs

Line 482 in 4fee690

const edges = [...quiver.cells[level]];

and the visual level to choose which kind of arrow to output:

quiver/src/quiver.mjs

Lines 674 to 689 in 4fee690

	// tikz-cd only has supported for 1-cells and 2-cells...
	if (edge.options.level === 2) {
	if (edge.options.style.head.name === "none") {
	// We special-case the combination of double arrows with no head,
	// because tikz-cd has a dedicated style, which means more concise
	// output.
	parameters.equals = "";
	} else {
	parameters.Rightarrow = "";
	}
	} else if (edge.options.level > 2) {
	// So for n-cells for n > 2, we make use of tikz-nfold.
	parameters.Rightarrow = "";
	parameters["scaling nfold"] = edge.options.level;
	add_dependency("tikz-nfold", "triple arrows or higher");
	}

In the comments "k-cell" tends to refer generally to either an object or an edge, for which the actual level is k. Let me know if you have any other questions!