equivalence of 2-categories
lax natural transformation
Yoneda lemma for bicategories
fully faithful morphism
fibration in a 2-category
pseudoalgebra for a 2-monad
Gray tensor product
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higher category theory
associator , unitor, Jacobiator
A unitor in category theory and higher category theory is an isomorphism that relaxes the ordinary uniticity equality of a binary operation.
In a bicategory the composition of 1-morphisms does not satisfy uniticity as an equation, but ther are natural unitor 2-morphisms
that satisfy a coherence law among themselves.
By the periodic table of higher categories a monoidal category is a pointed bicategory with a single object, its objects are the 1-morphisms of the bicategory.
Accordingly, a monoidal category is equipped with a natural isomorphism
called the left unitor, and a natural isomorphism
called the right unitor.