nLab
exactness property

Context

Regular and Exact categories

κ-ary regular and exact categories

regularity

exactness

Limits and colimits

Category theory

Exactness properties

Idea

An exactness property of a category asserts the existence of certain limits and colimits, and moreover that the limits and colimits interact in a certain way. Frequently, this includes stability of the colimits under pullback, and also a condition expressing that some of the input data can be recovered from the colimit.

Many types of exactness can be expressed in terms of “colimits in the left-exact world”.

Exactness properties of a functor refer to preservation of limits or colimits of certain kind, existence of adjoints and possibly their exactness properties.

Examples

References

Revised on February 23, 2013 07:44:29 by Mike Shulman (192.16.204.218)