In mathematics, a tricategory is a kind of structure of category theory studied in higher-dimensional category theory.

Whereas a weak 2-category is said to be a bicategory,[1] a weak 3-category is said to be a tricategory (Gordon, Power & Street 1995; Baez & Dolan 1996; Leinster 1998).[2][3][4]

Tetracategories are the corresponding notion in dimension four. Dimensions beyond three are seen as increasingly significant to the relationship between knot theory and physics. John Baez, R. Gordon, A. J. Power and Ross Street have done much of the significant work with categories beyond bicategories thus far.

See also


  1. ^ Bénabou, Jean (1967). "Introduction to bicategories". Reports of the Midwest Category Seminar. Lecture Notes in Mathematics. Vol. 47. Springer Berlin Heidelberg. pp. 1–77. doi:10.1007/bfb0074299. ISBN 978-3-540-03918-1.
  2. ^ Gordon, R.; Power, A. J.; Street, Ross (1995). "Coherence for tricategories". Memoirs of the American Mathematical Society. 117 (558). doi:10.1090/memo/0558. ISSN 0065-9266.
  3. ^ Baez, John C.; Dolan, James (10 May 1998). "Higher-Dimensional Algebra III.n-Categories and the Algebra of Opetopes". Advances in Mathematics. 135 (2): 145–206. arXiv:q-alg/9702014. doi:10.1006/aima.1997.1695. ISSN 0001-8708.
  4. ^ Leinster, Tom (2002). "A survey of definitions of n-category". Theory and Applications of Categories. 10: 1–70. arXiv:math/0107188.