What does bicategory mean?
Definitions for bicategory
bi·cat·e·go·ry
This dictionary definitions page includes all the possible meanings, example usage and translations of the word bicategory.
Wiktionary
bicategorynoun
A particular construct in category theory
Wikidata
Bicategory
In mathematics, a bicategory is a concept in category theory used to extend the notion of category to handle the cases where the composition of morphisms is not associative, but only associative up to an isomorphism. The notion was introduced in 1967 by Jean Bénabou. Formally, a bicategory B consists of: ⁕objects a, b... called 0-cells; ⁕morphisms f, g, ... with fixed source and target objects called 1-cells; ⁕"morphisms between morphisms" ρ, σ... with fixed source and target morphisms, called 2-cells; with some more structure: ⁕given two objects a and b there is a category B whose objects are the 1-cells and morphisms are the 2-cells, the composition in this category is called vertical composition; ⁕given three objects a, b and c, there is a bifunctor called horizontal composition. The horizontal composition is required to be associative up to a natural isomorphism α between morphisms and . Some more coherence axioms, similar to those needed for monoidal categories, are moreover required to hold. Bicategories may be considered as a weakening of the definition of 2-categories. A similar process for 3-categories leads to tricategories, and more generally to weak n-categories for n-categories.
Numerology
Chaldean Numerology
The numerical value of bicategory in Chaldean Numerology is: 2
Pythagorean Numerology
The numerical value of bicategory in Pythagorean Numerology is: 6
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"bicategory." Definitions.net. STANDS4 LLC, 2024. Web. 25 Apr. 2024. <https://www.definitions.net/definition/bicategory>.
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