Tom Leinster

**N = 0 : 0-Cat**

- => Set, 0-morphism = function

**N= 1: 1-Cat**

- => Cat, 1-morphism = functor

**N= 2: 2-Cat**

- => 2-morphism = Natural Transformation

$latex text {f, g : 1-morphism }$

$latex alpha :: beta text { Natural Transformations : 2-morphism }$

**Definition of n-Category:**

**Composition**:

0-Cat : Set

1-Cat : Cat

**Examples of n-Categories:**

**Manifold****Top (**Topological Space**) :***2-morphism = homotopy*

**Ref**:

Best Technical Category Theory Book (2016) by Tom Leinster (Cambridge Press): “Basic Category Theory”

(Free downloadfrom arxiv)