(Co)end Calculus

The language of ends and (co)ends provides a natural and general way of expressing many phenomena in category theory, in the abstract and in applications.Yet although category-theoretic methods are now widely used by mathematicians, since (co)ends lie just beyond a first course in category theory, they are typically only used by category theorists, for whom they are something of a secret weapon.This book is the first systematic treatment of the theory of (co)ends.Aimed at a wide audience, it presents the (co)end calculus as a powerful tool to clarify and simplify definitions and results in category theory and export them for use in diverse areas of mathematics and computer science.It is organised as an easy-to-cite reference manual, and will be of interest to category theorists and users of category theory alike.