Николай Иваныч (nivanych) wrote in category_theory,
Николай Иваныч

This is the (co)end, my only (co)friend

"Раз пошла такая пьянка" и у ivan_gandhi
в его блоге постоянно стали упоминаться
(ко)концы и расширения Кана, то возник повод
вспомнить и про соответствующую статью ;-)
Кое-кто будет на неё ругаться и даже обзываться,
но я таки отрекламирую —

This is the (co)end, my only (co)friend
Fosco Loregian
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.
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