Category 0 information

Category 0 can refer to: Empty category 0, the category of no objects and no morphisms, is the initial object of the category of small categories is the...

 111. ISBN 0-201-14236-8. Cheng 2017, p. 60. Kardar 2007, p. 35. Riehl, Emily (2016). Category Theory in Context. Dover. p. 103. ISBN 978-0-486-80903-8...

the empty category 0, which is the category of no objects and no morphisms. The terminal object is the terminal category or trivial category 1 with a single...

In algebra, given a ring R, the category of left modules over R is the category whose objects are all left modules over R and whose morphisms are all...

Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the...

scales Category 3 pandemic, on the Pandemic Severity Index, an American influenza pandemic with a case-fatality ratio between 0.5% and 1% Category 3 winter...

A Category 5 Atlantic hurricane is a tropical cyclone that reaches Category 5 intensity on the Saffir–Simpson hurricane wind scale, within the Atlantic...

0 ≤ i < n (both directions are allowed in the same sequence). Equivalently, a category J is connected if each functor from J to a discrete category is...

scales Category 2 pandemic, on the Pandemic Severity Index, an American influenza pandemic with a case-fatality ratio between 0.1% and 0.5% Category 2 winter...

scales Category 1 pandemic, on the Pandemic Severity Index, an American influenza pandemic with a case-fatality ratio of less than 0.1% Category 1 winter...

000 lb) Category N3: having a maximum mass exceeding 12 tonnes Category O: trailers (including semi-trailers) Category O1: maximum mass not exceeding 0.75...

well-behaved type of morphism. A normal category is a category in which every monomorphism is normal. A conormal category is one in which every epimorphism...

specifically in category theory, a preadditive category is another name for an Ab-category, i.e., a category that is enriched over the category of abelian...

In mathematics, a monoidal category (or tensor category) is a category C {\displaystyle \mathbf {C} } equipped with a bifunctor ⊗ : C × C → C {\displaystyle...

prototypical example of an abelian category is the category of abelian groups, Ab. Abelian categories are very stable categories; for example they are regular...

2-morphisms, the category n-Cat of (small) n-categories is actually an (n + 1)-category. An n-category is defined by induction on n by: A 0-category is a set...

many categories in mathematics, the category of rings is large, meaning that the class of all rings is proper. The category Ring is a concrete category meaning...

IUCN protected area categories, or IUCN protected area management categories, are categories used to classify protected areas in a system developed by...

In mathematics, the derived category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense...

2021. Awodey, Steve (2010). Category Theory (2 ed.). Oxford, UK: Oxford University Press. pp. xv, 1–336. ISBN 978-0-19-958-736-0. Zbl 1291.00036. Blokhintsev...

In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets. The arrows or morphisms between...

A category killer is a retailer, often a big-box store, that specializes in and carries a large product assortment of a given category.: 109–111  Through...

and 0 when X is not equal to Y. Some authors prefer a weaker notion, where a discrete category merely needs to be equivalent to such a category. Any...

In ontology, the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities according to Amie Thomasson...

In mathematics, a complete category is a category in which all small limits exist. That is, a category C is complete if every diagram F : J → C (where...