Exact Sequences and Regular Functors
In a regular category, a diagram of the form is said to be an exact sequence if it is both a coequalizer and a kernel pair. The terminology is a generalization of exact sequences in homological algebra: in an abelian category, a diagram
is exact in this sense if and only if is a short exact sequence in the usual sense.
A functor between regular categories is called regular, if it preserves finite limits and coequalizers of kernel pairs. A functor is regular if and only if it preserves finite limits and exact sequences. For this reason, regular functors are sometimes called exact functors. Functors that preserve finite limits are often said to be left exact.
Read more about this topic: Regular Category
Famous quotes containing the words exact and/or regular:
“Hunger makes you restless. You dream about food—not just any food, but perfect food, the best food, magical meals, famous and awe-inspiring, the one piece of meat, the exact taste of buttery corn, tomatoes so ripe they split and sweeten the air, beans so crisp they snap between the teeth, gravy like mother’s milk singing to your bloodstream.”
—Dorothy Allison (b. 1953)
“It was inspiriting to hear the regular dip of the paddles, as if they were our fins or flippers, and to realize that we were at length fairly embarked. We who had felt strangely as stage-passengers and tavern-lodgers were suddenly naturalized there and presented with the freedom of the lakes and woods.”
—Henry David Thoreau (1817–1862)