The periodic table of n-categories for low dimensions I: degenerate categories and degenerate bicategories

  title={The periodic table of n-categories for low dimensions I: degenerate categories and degenerate bicategories},
  author={Eugenia Cheng and Nick Gurski},
  journal={arXiv: Category Theory},
We examine the periodic table of weak n-categories for the low-dimensional cases. It is widely understood that degenerate categories give rise to monoids, doubly degenerate bicategories to commutative monoids, and degenerate bicategories to monoidal categories; however, to understand this correspondence fully we examine the totalities of such structures together with maps between them and higher maps between those. Categories naturally form a 2-category {\bfseries Cat} so we take the full sub-2… 

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