Image (category theory)

In category theory is an image of a morphism a sub-object of which has the following universal property:

• There is a morphism with.
• For each subobject that meets the above property ( ), there is a unique morphism with and.

The Kobild a morphism is the dual concept: a Kobild is a quotient object of X, which has the following universal property:

• There is a morphism Intl.
• For each quotient object that satisfies the above property ( ), there is a unique morphism with and.

In categories with core and cokernel of each core of a Kokerns of an image f of f, every cokernel of the core is a Kobild.

In abelian categories as the categories of vector spaces or Abelian groups are consistent picture and Kobild. In each of these categories, they are also equal to the set-theoretic image.

• Category theory