F eb 2 01 5 THIS IS THE ( CO ) END , MY ONLY ( CO ) FRIEND

The present note is a recollection of the most striking and useful applications of co/end calculus. We put a considerable effort in making arguments and constructions rather explicit: after having given a series of preliminary definitions, we characterize co/ends as particular co/limits; then we derive a number of results directly from this characterization. The last sections discuss the most interesting examples where co/end calculus serves as a powerful abstract way to do explicit computations in diverse fields like Algebra, Algebraic Topology and Category Theory. The appendices serve to sketch a number of results in theories heavily relying on co/end calculus; the reader who dares to arrive at this point, being completely introduced to the mysteries of co/end fu, can regard basically every statement as a guided exercise.