Tricategory Explained

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

• Weak n-category

External links

• The Dimensional Ladder
• Branches of higher dimensional algebra

Notes and References

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