3-category

In mathematics, especially in category theory, a 3-category is a 2-category together with 3-morphisms. It comes in at least three flavors

  • a strict 3-category,
  • a semi-strict 3-category also called a Gray category,
  • a weak 3-category.

The coherence theorem of Gordon–Power–Street says a weak 3-category is equivalent (in some sense) to a Gray category.

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