[**Continued** from previous BM Category Theory …]

$latex boxed {

text {type Algebra f a = f a} to text {a}

}&fg=aa0000&s=3$

Intuition:[Artificial Intelligence] You teach the computer, like a Primary 6 kid, thatAlgebrais atypeof expression(f) which, after evaluation, returns a value.

**If a = i (initial)***[or u (terminal)]*,

$latex boxed {

text {(f i} to text {i )} implies

text {f = Fix-point}

}&fg=0000aa&s=3$

**Intuition**: *Fix-point because, the Initial “i” after the evaluating the expression f, returns itself “i”.*

**Lambek’s Lemma**

$latex boxed {

text {Endo-functor = Isomormphism}

}&fg=00aa00&s=3$

**Note**: Endo-functor is a **functor** (equivalent to*function *in Set Theory) within the same Category (Endo = Self = 自)

Video 8.1F-Algebras & Lambek’s Lemma

Video 8.2Catamorphism & Anamorphism

foldr ~ catamorphism (浅层变质) of a Fix-point endo-functor on a List.

**Examples**: Fibinacci, Sum_List

View original post 147 more words