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A variable used to associate each data point in a set of observations, or in a particular instance, to a certain qualitative category is a categorical variable. Categorical variables have two types of scales, ordinal and nominal. [1] The first type of categorical scale is dependent on natural ordering, levels that are defined by a sense of quality.
Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, due to their numerical nature.
The class of all groups with group homomorphisms as morphisms and function composition as the composition operation forms a large category, Grp. Like Ord, Grp is a concrete category. The category Ab, consisting of all abelian groups and their group homomorphisms, is a full subcategory of Grp, and the prototype of an abelian category.
To give an example, the logical function behind our reasoning from ground to consequence (based on the Hypothetical relation) underlies our understanding of the world in terms of cause and effect (the Causal relation). In each table the number twelve arises from, firstly, an initial division into two: the Mathematical and the Dynamical; a ...
The zero objects in Grp are the trivial groups (consisting of just an identity element). Every morphism f : G → H in Grp has a category-theoretic kernel (given by the ordinary kernel of algebra ker f = { x in G | f ( x ) = e }), and also a category-theoretic cokernel (given by the factor group of H by the normal closure of f ( G ) in H ).
Every geometric cohomology theory is a functor on the category of motives. Each induced functor ρ:motives modulo numerical equivalence→graded Q-vector spaces is called a realization of the category of motives, the inverse functors are called improvements. Mixed motives explain phenomena in as diverse areas as: Hodge theory, algebraic K ...
In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the Cartesian product of sets, the direct product of groups or rings, and the product of topological spaces.
In archaeology, absolute dating is usually based on the physical, chemical, and life properties of the materials of artifacts, buildings, or other items that have been modified by humans and by historical associations with materials with known dates (such as coins and historical records). For example, coins found in excavations may have their ...