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Tytuł: Object-Free Definition of Categories
Autorzy: Riccardi, Marco
Słowa kluczowe: object-free category
correspondence between different approaches to category
Data wydania: 2013
Data dodania: 9-gru-2015
Wydawca: De Gruyter Open
Źródło: Formalized Mathematics, Volume 21, Issue 3, 2013, Pages 193-205
Abstrakt: Category theory was formalized in Mizar with two different approaches [7], [18] that correspond to those most commonly used [16], [5]. Since there is a one-to-one correspondence between objects and identity morphisms, some authors have used an approach that does not refer to objects as elements of the theory, and are usually indicated as object-free category [1] or as arrowsonly category [16]. In this article is proposed a new definition of an object-free category, introducing the two properties: left composable and right composable, and a simplification of the notation through a symbol, a binary relation between morphisms, that indicates whether the composition is defined. In the final part we define two functions that allow to switch from the two definitions, with and without objects, and it is shown that their composition produces isomorphic categories.
Afiliacja: Via del Pero 102 54038 Montignoso Italy
DOI: 10.2478/forma-2013-0021
ISSN: 1426-2630
Typ Dokumentu: Article
Występuje w kolekcji(ach):Formalized Mathematics, 2013, Volume 21, Issue 3

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