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

• Published in 2015
• Added on 2015-01-13

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.

Links

• http://arxiv.org/abs/1501.02503
• http://arxiv.org/pdf/1501.02503v2

Other information

BibTeX entry

@article{Loregian2015,
	key = {Loregian2015},
	type = {article},
	title = {This is the (co)end, my only (co)friend},
	author = {Loregian, Fosco},
	abstract = {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.},
	comment = {},
	date_added = {2015-01-13},
	date_published = {2015-01-01},
	urls = {http://arxiv.org/abs/1501.02503,http://arxiv.org/pdf/1501.02503v2},
	collections = {Attention-grabbing titles},
	month = {jan},
	pages = 39,
	url = {http://arxiv.org/abs/1501.02503 http://arxiv.org/pdf/1501.02503v2},
	year = 2015,
	archivePrefix = {arXiv},
	eprint = {1501.02503},
	primaryClass = {math.CT},
	urldate = {2015-01-13}
}