Category vs Multicategory - What's the difference?
category | multicategory |
A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
*
(mathematics) A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.
(mathematics) A generalization of the concept of category that allows morphisms of multiple arity
In mathematics|lang=en terms the difference between category and multicategory
is that category is (mathematics) a collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative while multicategory is (mathematics) a generalization of the concept of category that allows morphisms of multiple arity.As nouns the difference between category and multicategory
is that category is a group, often named or numbered, to which items are assigned based on similarity or defined criteria while multicategory is (mathematics) a generalization of the concept of category that allows morphisms of multiple arity.category
English
(wikipedia category)Noun
(categories)- The traditional way of describing the similarities and differences between constituents is to say that they belong to categories'' of various types. Thus, words like ''boy'', ''girl'', ''man'', ''woman'', etc. are traditionally said to belong to the category''' of Nouns, whereas words like ''a'', ''the'', ''this'', and ''that'' are traditionally said to belong to the ' category of Determiners.
- This steep and dangerous climb belongs to the most difficult category .
- I wouldn't put this book in the same category as the author's first novel.
- One well-known category has sets as objects and functions as arrows.
- Just as a monoid consists of an underlying set with a binary operation "on top of it" which is closed, associative and with an identity, a category consists of an underlying digraph with an arrow composition operation "on top of it" which is transitively closed, associative, and with an identity at each object. In fact, a category's composition operation, when restricted to a single one of its objects, turns that object's set of arrows (which would all be loops) into a monoid.