Universal Property
Explicitly, the pushout of the morphisms f and g consists of an object P and two morphisms i1 : X → P and i2 : Y → P for which the following diagram commutes:
Moreover, the pushout (P, i1, i2) must be universal with respect to this diagram. That is, for any other such set (Q, j1, j2) for which the following diagram commutes, there must exist a unique u : P → Q also making the diagram commute:
As with all universal constructions, the pushout, if it exists, is unique up to a unique isomorphism.
Read more about this topic: Pushout (category Theory)
Famous quotes containing the words universal and/or property:
“A universal and perpetual peace, it is to be feared, is in the catalogue of events which will never exist but in the imaginations of visionary philosophers, or in the breasts of benevolent enthusiasts.”
—James Madison (1751–1836)
“All over this land women have no political existence. Laws pass over our heads that we can not unmake. Our property is taken from us without our consent. The babes we bear in anguish and carry in our arms are not ours.”
—Lucy Stone (1818–1893)