In homological algebra, an exact functor is a functor that preserves exact sequences. Exact functors are convenient for algebraic calculations because they can be more directly applied to presentations of objects. Much of the work in homological algebra is designed to cope with functors that fail to be exact, but in ways that can still be controlled.
Other articles related to "exact functor, exact functors, functor, exact, functors":
... In SGA4, tome I, section 1, the notion of left (right) exact functors are defined for general categories, and not just abelian ones ... Then a functor u from C to another category C′ is left (resp ... right) exact if it commutes with projective (resp ...
... but in the behavior of the resolution with respect to a given functor ... Therefore, in many situations, the notion of acyclic resolutions is used given a left exact functor F A → B between two abelian categories, a resolution of an object M of A is called F-acyclic, if the derived ... Dually, a left resolution is acyclic with respect to a right exact functor if its derived functors vanish on the objects of the resolution ...
Famous quotes containing the word exact:
“To conclude, The Light of humane minds is Perspicuous Words, but by exact definitions first snuffed, and purged from ambiguity; Reason is the pace; Encrease of Science, the way; and the Benefit of man-kind, the end.”
—Thomas Hobbes (15791688)