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 point of view, category, theory, point and/or view:
“At this age [9–12], in contrast to adolescence, girls still want to know their parents and hear what they think. You are the influential ones if you want to be. Girls, now, want to hear your point of view and find out how you got to be what you are and what you are doing. They like their fathers and mothers to be interested in what they’re doing and planning. They like to know what you think of their thoughts.”
—Stella Chess (20th century)
“The truth is, no matter how trying they become, babies two and under don’t have the ability to make moral choices, so they can’t be “bad.” That category only exists in the adult mind.”
—Anne Cassidy (20th century)
“Don’t confuse hypothesis and theory. The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.”
—Martin H. Fischer (1879–1962)
“When raging love with extreme pain
Most cruelly distrains my heart,
When that my tears, as floods of rain,
Bear witness of my woeful smart;
When sighs have wasted so my breath
That I lie at the point of death,”
—Henry Howard, Earl Of Surrey (1517?–1547)
“Bias, point of view, fury—are they ... so dangerous and must they be ironed out of history, the hills flattened and the contours leveled? The professors talk ... about passion and point of view in history as a Calvinist talks about sin in the bedroom.”
—Catherine Drinker Bowen (1897–1973)