It is evident from contemporary mathematical practice that there does not exist any usual notation to denote that a diagram commutes. This is almost always stated in meta-language above or below a diagram.
Questions. Is there anything even close to a standard symbolic notation to indicate that a diagram commutes? Maybe in higher category theory?
Is there any noteworthy book or paper which makes use of a symbol, regardless of whether this is to be considered standard or advisable, instead of using surrounding words to impose the condition of commmutativity?
Part of the motivation for this question is wishing not to have to make up a symbol if there is any noteworthy precedent in the literature, but, needless to say, I have never seen any such.
Since there is e.g. a standard symbol to denote pullback diagrams, it seems somewhat surprising that the contemporary consensus seems to be to use surrounding words instead of a symbol.
Of couse, the omission of certain composite morphisms in a diagram can be seen as some sort of signalling that a diagram is required to commute. The iconic example is a commutative square, in which, for good reason, the two composites are not drawn, and one could see this very omission to by indicative enough. Yet, to me, this seems not to yield a precise pictorial language, least of all when it comes to using diagrams as input to machine-computations.
- I seem to recall to have once read a paper, which I do not find, saying that in the early days of category theory the writing style in books and papers was more diagrammatical than nowadays, so, it at all, a notational convention such as the one I am looking for might be found in early category theoretical papers.