In category theory , a natural numbers object ( NNO ) is an object endowed with a recursive structure similar to natural numbers . More precisely, in a category E with a terminal object 1, an NNO N is given by:
4-546: NNO may stand for: Nuveen North Carolina Dividend Advantage Municipal Fund 2 (stock symbol: NNO) Natural number object , in category theory , a subfield of mathematics National Night Out , a crime prevention activity in the United States Nynorsk , ISO 639-2 and ISO 639-3 language codes Nitrous oxide Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with
8-436: A unique arrow u : N → A such that: In other words, the triangle and square in the following diagram commute. The pair ( q , f ) is sometimes called the recursion data for u , given in the form of a recursive definition : The above definition is the universal property of NNOs, meaning they are defined up to canonical isomorphism . If the arrow u as defined above merely has to exist, that is, uniqueness
12-458: Is not required, then N is called a weak NNO. NNOs in cartesian closed categories (CCCs) or topoi are sometimes defined in the following equivalent way (due to Lawvere ): for every pair of arrows g : A → B and f : B → B , there is a unique h : N × A → B such that the squares in the following diagram commute. This same construction defines weak NNOs in cartesian categories that are not cartesian closed. In
16-562: The title NNO . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=NNO&oldid=895958004 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Natural number object such that for any object A of E , global element q : 1 → A , and arrow f : A → A , there exists
#797202