Category Theory Point of View
In category theory the disjoint union is defined as a coproduct in the category of sets.
As such, the discrete union is defined up to an isomorphism, and the above definition is just one realization of the coproduct, among others. When the sets are pairwise disjoint, the usual union is another realization of the coproduct. This justifies the second definition in the lead.
This categorical aspect of the discrete union explains why is frequently used, instead of, to denote it.
Read more about this topic: Disjoint Union
Famous quotes containing the words category, theory, point and/or view:
“I see no reason for calling my work poetry except that there is no other category in which to put it.”
—Marianne Moore (1887–1972)
“every subjective phenomenon is essentially connected with a single point of view, and it seems inevitable that an objective, physical theory will abandon that point of view.”
—Thomas Nagel (b. 1938)
“Mildred Pierce: You look down on me because I work for a living, don’t you? You always have. All right, I work. I cook food and sell it and make a profit on it, which, I might point out, you’re not too proud to share with me.
Monte Beragon: Yes, I take money from you, Mildred. But not enough to make me like kitchens or cooks. They smell of grease.
Mildred Pierce: I don’t notice you shrinking away from a fifty- dollar bill because it smells of grease.”
—Ranald MacDougall (1915–1973)
“My tendency to nervousness in my younger days, in view of the fact of a number of near relatives on both my father’s and mother’s side of the house having become insane, gave some serious uneasiness. I made up my mind to overcome it.... In the cross-examination of witnesses before a crowded court-house ... I soon found I could control myself even in the worst of testing cases. Finally, in battle.”
—Rutherford Birchard Hayes (1822–1893)