Categories

Guerino Mazzola, Maria Mannone, Yan Pang

Music (Twin Cities)

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We have often referred to certain types of Fig. 29.1. Categories are the smiley of contemporary mathematics. structures—sets, monoids, groups, rings, digraphs, or modules—where there was a shared structural characteristic: All of these structures have objects (such as sets, monoids, groups, etc.) and a type of “function” (set functions, monoid morphisms, digraph morphisms, etc.). And all of these functions can be composed if domains and codomains can be ‘concatenated.’ The common denominator of these structures is the concept of a category.

Original language	English (US)
Title of host publication	Computational Music Science
Publisher	Springer Nature
Pages	249-254
Number of pages	6
DOIs	https://doi.org/10.1007/978-3-319-42937-3_29
State	Published - 2016

Publication series

Name	Computational Music Science
ISSN (Print)	1868-0305
ISSN (Electronic)	1868-0313

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing Switzerland.

Keywords

Commutative Ring
Forgetful Functor
Local Composition
Natural Transformation
Usual Perspective

Publisher link

10.1007/978-3-319-42937-3_29

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Cite this

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AU - Mannone, Maria

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KW - Usual Perspective

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