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> A category consists of abstract functions (or morphisms, or “arrows”) that have an origin and destination (or domain and codomain, or “argument type” and “ret
by scandox 10y ago
> A category consists of abstract functions (or morphisms, or “arrows”) that have an origin and destination (or domain and codomain, or “argument type” and “return type”).
I think perhaps Maths people need to seek more consensus on terminology.
- shmageggy 10y agoSeriously. I've tried to read on category theory before and never really grokked what it was all about. The sentence you quoted was literally the first one I've ever read that actually made me say, "oh, that's what this is".
- houli 10y agoThe category theory idea of a morphism is more abstract than a function. If functions deal with domains and codomains then certainly morphisms need new words to deal with the abstractions of those ideas that are specific to functions.
- mikebenfield 10y agoI've only seen mathematicians use the terms morphisms, arrows, and domain/codomain. It is true that morphisms and arrows mean the same thing, but I think that's because the term morphism is specific to category theory and the term arrow is from graph theory. All the other terms here (abstract functions, origin, destination, argument type, return type) appear to be the author's attempt to make the subject understandable to programmers.
- johnloeber 10y agoThe term "arrow" is from category theory, not graph theory.
- fabianhjr 10y agoMorphism is from Algebra/General Mathematics and it is a function that preserves a "structure". (Group Morphism, Isomorphism between sets, etc) In Graph Theory the terminology is Node and Vertex. Arrow, Source and Target are from Category Theory.
- tel 10y agoMorphism is the standard general term. If you have a collection of objects with the some sort of structure then a morphism maps one of those to another preserving that structure. In CT you usually are dealing with morphisms, but not always and that intuition can get in your way. For this reason, arrow is sometimes used instead to indicate something a little more abstract than morhism.
- JadeNB 10y ago> I think perhaps Maths people need to seek more consensus on terminology. If only they could follow the example of programmers, who never have two different words for identical (or, worse, near-identical) concepts!
- eru 10y agoI find the opposite worse: using the same term for different concepts. (I am looking at you, C++ people, and your so called "Functors"!)
- fabianhjr 10y agoWell you will normally see two terminologies: - Morphism (Domain, Codomain) - Arrow (Source, Target) The reason for the last one is that you may find "Arrows" that aren't functions. (Such as an order relationship in the Poset category)
- wetmore 10y agoMorphisms are not necessarily functions either.