homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
In a higher category, invertibility of n-morphisms in its highest dimension is always considered strictly. Thus in an ordinary category, we have 1-morphisms which can be isomorphisms. In a 2-category, it is the 2-morphisms for which, when it comes to invertibility, we always ask for a strict inverse, whereas for 1-morphisms we typically ask only for an equivalence. These 2-morphisms which admit an inverse are known as 2-isomorphisms.
Let be a 2-category. A 2-isomorphism in is a 2-arrow of which admits a (strict) inverse, that is to say, there is a 2-arrow of such that and .
A 2-category in which every 2-arrow is a 2-isomorphism is known as a (2,1)-category.
Last revised on July 4, 2020 at 17:50:55. See the history of this page for a list of all contributions to it.