A strict morphism is a morphism for which the notion of image and coimage coincide.
Compare with strict epimorphism.
In a category with limits and colimits
Let be a category with finite limits and colimits. Let be a morphism in .
Recall that the image of is the limit
i.e. the equalizer of ,
while the coimage is the colimit
By the various universal properties, there is a unique morphism
The morphism is called a strict morphism if is an isomorphism.
Examples of categories in which every morphism is strict include
Revised on July 9, 2010 07:23:40
by Urs Schreiber