Pullback

In mathematics, a pullback is either of two different, but related processes: precomposition and fibre-product. Its 'dual' is a pushforward. In mathematics, a pullback is either of two different, but related processes: precomposition and fibre-product. Its 'dual' is a pushforward. Precomposition with a function probably provides the most elementary notion of pullback: in simple terms, a function f of a variable y, where y itself is a function of another variable x, may be written as a function of x. This is the pullback of f by the function y. It is such a fundamental process, that it is often passed over without mention. It pervades areas as diverse as fluid mechanics and differential geometry. However, it is not just functions that can be 'pulled back' in this sense. Pullbacks can be applied to many other objects such as differential formsand their cohomology classes.