A lift or lifting of a morphism (in some category) through an epimorphism (or more general map) , is a morphism such that :
This is the concept formally dual to extension.
More generally, given a square commuting diagram, then one says a lift in the diagram is a dashed morphism from the bottom left to the top right, making both resulting triangles commute:
This reduces to the previous situation in the case that is an initial object. (Whereas, when is a terminal object then it reduces to the situation of an extension).
If such a lift exists at all, one also says that has the left lifting property against , and equivalently that has the right lifting property against .
Last revised on October 15, 2024 at 18:03:56. See the history of this page for a list of all contributions to it.