Equaliser (mathematics)

A difference kernel (also: Egalisator, English:. Equalizer ) is a generalization of the mathematical concept of core to any categories.

The core of a pair of differential images between the two sets, and the subset of, and at the same, i.e.,

A core difference of two morphisms in any category is characterized by the following equivalent properties of sub-object:

• And to each arrow, is for him there is exactly one arrow, so that.

In which

And is the difference kernel on the right side of the core difference described above in the category of sets, not considered in this category.

Furthermore, the isomorphism in point 2 should be natural, that is to say: If we call the family of isomorphisms

Then for any and all defined for the following expression that

Examples

In the categories of groups, abelian groups, vector spaces or rings is the core difference of two morphisms of the underlying lot of pictures.

• Category theory