Bartosz Milewski on Nostr: Stupid math question: In one of my blogs I claimed that if there are two parallel ...

Stupid math question: In one of my blogs I claimed that if there are two parallel morphism f and g, whose composites on both left and right are always equal, that there is no way to distinguish between them, in THAT category. But you can always use a functor to a larger category, in which their images can compose differently, giving rise to different buidups of composites. (Below is an example of a 3-object category and its functorial mapping.)

Does it make sense? Is there a formal way of saying that two different morphisms are indistinguishable in a particular category? Are morphisms distinguishable if their sieves are not isomorphic?