File:Category_SVG.svg · Wikimedia Commons · See Wikimedia Commons
category
Sign in to savealgebraic structure of objects and morphisms between objects, which can be associatively composed if the (co)domains agree
Wikidata facts
- Has part
- morphism
- Followed by
- strict 2-category
- Follows
- class
- Image
- Category SVG.svg
Show 8 more facts
- discoverer or inventor
- Saunders Mac Lane
- time of discovery or invention
- 1945-00-00
- different from
- Category
- studied by
- category theory
- series ordinal
- 1
- on focus list of Wikimedia project
- Wikipedia:Vital articles/Level/4
- maintained by WikiProject
- WikiProject Mathematics
- quantity symbol (string)
- C
via Wikidata · CC0
~21 min read
Encyclopedic overview
This is a category with a collection of objects A, B, C and collection of morphisms denoted f, g, g ∘ f, and the loops are the identity arrows. This category is typically denoted by a boldface 3.
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A simple example is the category of sets, whose objects are sets and whose arrows are functions.
Excerpted from Wikipedia’s “category” article, available under the CC BY-SA 4.0 licence.