**“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 categoriesfunctor 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 naturallytheLadderto theStaircase.