Timeline for Why does the category of language types have morphisms, not functors?

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Dec 16, 2019 at 18:56	comment	added	Bartosz Milewski		List of int is just like string. In fact, in Haskell, String is defined as a list of Char. List of `a`, where `a` is not specified, is an (endo-) functor because it maps all objects (types) `a` to objects (types). It maps int to list of int, char to list of char, and so on. It's like `f(x)` with `x` being arbitrary vs. `f(42)`.
Dec 16, 2019 at 15:56	vote	accept	Crell
Dec 15, 2019 at 17:17	comment	added	Crell		Thanks! So if I follow correctly, it's valid to use either of the first two perspectives depending on what it is you want to describe? So an string->int function is a morphism and a string->string function an endomorphism, but they're not useful to think of as a functor even though you could. But "int with null" or "list of int" are valid alternate categories, which you can convert to with a functor. Following? (Context: I'm reading your book and trying to translate the concepts for PHP devs. Because I'm that kind of crazy.)
Dec 15, 2019 at 5:16	history	answered	Bartosz Milewski	CC BY-SA 4.0