[Continued from (Part I)…]

**Category Theory (范畴学)** is the *“lingua franca” *(通用语) of mathematicians, used commonly by the 2 different major Math branches : Algebra & Analysis.

**比喻**:

武术分”外家拳”少林派, “内家拳” 武当派。

两家的* lingua franca* (通用语)是 “**气**” – 硬气功(少林), 柔气功(武当)。

In essence: A Category consists of

1. Objects

2. Relationship among objects (Morphism)

3. Structure: preserved by Morphism

4. An identity (Self)

Examples:

1. **SET Category**:

◇ Objects (Sets),

◇ Structure (Cardinality),

◇ Morphism (Set Functions: which preserve Set Structure)

◇ Identity (Set itself)

2. **GROUP Category**

◇ Objects (groups)

◇ Structure (Set, 1 closed binary operation)

◇ Morphism (group mapping)

◇ Identity (neutral element ‘e’)

3. **SINGAPOREAN Category**

◇ Objects (Singapore citizens)

◇ Structure (multi-racial)

◇ Morphism (kiasu-ism)

◇ Identity (I = ME = 令伯 ‘lim-Peh-ism’)

Lecture 2:

◇ Functor: morphism between Categories

◇ Diagrams: arrows

◇ Commute

◇ __Special Types of Functors__:

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