“Categories for Dummies”
(French)
Example 1:
Paris (P) -> Rome (R) -> Amsterdam (A)
Objects: cities {P, R , A}
Morphism (Arrow): railway
- Identity: railway within the city
- Associative: (P -> R) -> A = P -> (R ->A)
=> Category
Example 2:
A, B are categories
functor f : A -> B
f (B) has the “information” on A, with some loss of information since f may not be a MONOMORPHISM.
Example 3: Natural Transformation
A = 0 1 2 3 4
f : A -> B
B = Ladder steps:
f(0)|
f(1)|
f(2)|
f(3)|
g : A -> B
B = Staircase steps :
g(0)||
g(1)||
g(2)||
g(3)||
Natural Transformation: =>α
α : f (i) => g (i)
f(0)| =>g(0)||
f(1)|=>g(1)||
f(2)|=>g(2)||
f(3)|=>g(3)||
α transforms naturally the Ladder to the Staircase.
Mathtuition88 