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)
