nLab weakly initial object



Category theory

Limits and colimits



An object in a category is weakly initial if there exists a morphism from it to every other object in the category.

(So a weakly initial object is an actual initial object if this morphism is unique.)

Weak initiality is an instance of a weak colimit. It is also an instance of a weakly initial set that happens to be a singleton set.


Weak adjoint functors along with weak colimits, with weakly initial objects as a special case, were defined in:

See also:

Last revised on April 22, 2023 at 13:32:50. See the history of this page for a list of all contributions to it.