I think we can sit here and speculate which properties of left inverses are actually important for quite a while. But we will only ever get a real answer to this question, when the original poster finishes formalizing…
> your fix kinda breaks a lot of the structure of algebra in other ways What are you referring to here in particular? I think the property of `g` to be a well defined function is a lot more important than for its domain…
Of course I can compose `f: A -> B` and `g: f(A) -> A`. The composition maps a `x` from `A` to `g(f(x))` which is well defined. Therefore the composition is a function. `g` and `f` aren't functions in a programming…
No, f can still map to `B` and does not need to be surjective. We just loosened the definition of `g` a little in a way that doesn't matter.
While the proposed fix of requiring "either that A be inhabited or that B be uninhabited" works, it seems tacked on just to solve this particular edge-case. I think a more elegant solution would be to soften the…
On a lot of linux distros there is the `moreutils` package, which contains a command called `chronic`. Originally intended to be used in crontabs, it executes a command and only outputs its output if it fails. I think…
I think we can sit here and speculate which properties of left inverses are actually important for quite a while. But we will only ever get a real answer to this question, when the original poster finishes formalizing…
> your fix kinda breaks a lot of the structure of algebra in other ways What are you referring to here in particular? I think the property of `g` to be a well defined function is a lot more important than for its domain…
Of course I can compose `f: A -> B` and `g: f(A) -> A`. The composition maps a `x` from `A` to `g(f(x))` which is well defined. Therefore the composition is a function. `g` and `f` aren't functions in a programming…
No, f can still map to `B` and does not need to be surjective. We just loosened the definition of `g` a little in a way that doesn't matter.
While the proposed fix of requiring "either that A be inhabited or that B be uninhabited" works, it seems tacked on just to solve this particular edge-case. I think a more elegant solution would be to soften the…
On a lot of linux distros there is the `moreutils` package, which contains a command called `chronic`. Originally intended to be used in crontabs, it executes a command and only outputs its output if it fails. I think…