[b3morales]

I agree, and not just the English. There is use of particular notation that does not explain anything unless you already know what it means:

> f is a morphism from a -> b, and g is a morphism from b -> c; g(f(x)) must be equivalent to (g • f)(x)

If I don't already understand (g • f)(x) this is not helpful at all. This other one especially jumped out at me (perhaps because I've personally never seen this "bent equals sign" ≍ before):

> A functor must adhere to two rules:

> Preserves identity

> object.map(x => x) ≍ object

What does that sign ≍ mean? If I don't know, I am no closer to understanding functors. And the sign is not explained anywhere in the document.

[cratermoon]

Oh boy. I didn't put on my glasses to read it so I didn't notice that ≍ is not = and that's important.

I think in the context it just means the result is in the range of "function applied to object"

[hither_shores]

> What does that sign ≍ mean?

Normally, `f ≍ g` means `f \in \Theta(g)`. Here, the author is using it as an equals sign. I have no idea why.

[cratermoon]

Except it's not and =, it's a ≍ sign, which looks almost identical. I'm not a mathematician and I don't know the deep theory behind functional programming, but the internet tells me that ≍ in Graham, Knuth, and Patashnik's Concrete Mathematics it's defined to mean the same thing as "Big Θ"[1], as you note.

1 https://math.stackexchange.com/questions/764897/what-does-th...