An Introduction to N-Categories

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

\text {f, g : 1-morphism } 

\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 download from arxiv)

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