- Adjoints as far as I understand are not about joining things, adjoints are about a generalization of inverses. Can you formally (and I mean mathematically) de

- Adjoints as far as I understand are not about joining things, adjoints are about a generalization of inverses. Can you formally (and I mean mathematically) define what this intuition you have about adjoints ~= "joining things"? Also, the word "adjoint" does not come from "join". It comes from "adjoint" in the theory of complex operators: https://en.wikipedia.org/wiki/Adjoint_functors https://en.wikipedia.org/wiki/Adjoint_functors - Homotopy is not about finding paths, it is an equvalence relation _between paths_. a path is _homotopic_ to another. Homotopy is also a _continuous object_, unlike torsors, which are discrete objects (a continuous torsor is an affine space). So, while UNIX paths and URLs are "paths" in the sense of torsors, they have _nothing_ to do with homotopy (as it is classically defined). Unless you are using some weakened notion of homotopy that I am unaware of, in which case I'd love links.