伟大的范畴理论

范畴理论是数学上的一种新的语言和框架结构. 对于程序员来说，它是另一种思考方式，一种极度有效的方式来提取规律(Extremely efficient for generalization) Programming is doing Math.编成的工作其实就是数学的工作。

范畴是一种表达事物(things) 和路径(ways) to go between things. 这可以参考thinking like a git，因为他也是一种基于范畴理论， 而延伸出来的实际产物，方便程序员对于development的管理。

A Category C is defined by:

• Objects ob(C),
• Morphisms hom(C),
• a Composition law (∘)

Functor : (ob->ob)

Functor : (hom->hom)

Endofunctors:

Categories and functors form a category: Cat

• ob(Cat) are categories
• hom(Cat) are functors
• ∘ is functor composition

A Haskell Functor is a type F :: * -> * which belong to the type class Functor ; thus instantiate fmap :: (a -> b) -> (F a -> F b).

• F: ob(Hask)→ob(Hask)
• & fmap: hom(Hask)→hom(Hask)

The couple (F,fmap) is a Hask’s functor if for any x :: F a:

fmap id x = x
fmap (f.g) x= (fmap f . fmap g) x