nLab 3-morphism

• object

• morphism

• 2-morphism

• 3-morphism

• k-morphism

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Definition

A 3-morphism in an n-category is a morphism between 2-morphisms.

Examples

For $A$ an abelian group, the 3-fold delooping $\mathbf{B}^3 A$ is a 3-groupoid whose 3-morphisms are given by $A$.