Definition
Limits and colimits in a category C are defined by means of diagrams in C. Formally, a diagram of type J in C is a functor from J to C:
- F : J → C.
The category J is thought of as index category, and the diagram F is thought of as indexing a collection of objects and morphisms in C patterned on J. The actual objects and morphisms in J are largely irrelevant—only the way in which they are interrelated matters.
One is most often interested in the case where the category J is a small or even finite category. A diagram is said to be small or finite whenever J is.
Read more about this topic: Limit (category Theory)
Famous quotes containing the word definition:
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)