Interesting notational workarounds for non-associativity, non-commutativity, residuals, adjoints (including logarithm-, root- and division-like ops) throughout mathematics?

This is a very general open-ended survey/discovery question and I already can predict the downvotes and toxic comments (as we always have) but I think it's appropriate for this subreddit as I would like to discover literature and get in touch with other areas of research. I could say one central theme of my research are residuated structures (lattices, algebras, categories), residuals and Galois connections/adjunctions. One of my main objectives is in making logic, category theory and formal methods in computer science accessible (thus coming from the pointfree transformation / calculational mathematics / Bird-Meertens / Algebra of Programming ideal) and residuated structures and adjunctions are indispensable to that objective. Sadly I feel first and second-year undergrads can feel very annoyed and confused by the simple fact of having two "division-like operations" (residuals) that most of the times can be calculated only up to inclusions/inequalities (even more than dealing with non-commutative multiplication-like operations - as anyone already do in linear algebra). I think this difficulty is very similar to that of high-schoolers and freshman calculus students (which I taught for a while) when dealing with similarly non-commutative and non-associative operations such as exponents and relating them to their differing badly notated inverses (logs and roots). I am already well aware of proposals for alternative notations for logarithms and roots (such as the triangle notation and this ) as well as proposals such as these for dealing with problems of non-associativity and non-commutativity of operations, but I would like to know: what are interesting approaches you know in the literature/that you are aware for dealing better with non-commutativity, non-associativity, multiplicity of inverses, residuals and adjoints as well as dealing with operations that are similarly defined only up to an inequality/inclusion/uni-directional mapping through an adjunction/Galois connection? I appreciate your suggestions.