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In cognitive psychology, a basic category is a category at a particular level of the category inclusion hierarchy (i.e., a particular level of generality) that is preferred by humans in learning and memory tasks.
Category theory was originally introduced for the need of homological algebra, and widely extended for the need of modern algebraic geometry (scheme theory). Category theory may be viewed as an extension of universal algebra, as the latter studies algebraic structures, and the former applies to any kind of mathematical structure and studies ...
Monomorphisms generalize this property to arbitrary categories. A morphism is a monomorphism if it is idempotent with respect to pullbacks. The categorical dual of a monomorphism is an epimorphism, that is, a monomorphism in a category C is an epimorphism in the dual category C op. Every section is a monomorphism, and every retraction is an ...
In ontology, the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities. [1] To investigate the categories of being, or simply categories , is to determine the most fundamental and the broadest classes of entities. [ 2 ]
Basic groups: The smallest possible social group with a defined number of people (i.e. greater than 1)—often associated with family building: Dyad : Will be a group of two people. Social interaction in a dyad is typically more intense than in larger groups as neither member shares the other's attention with anyone else.
He published textbooks on category theory [2] and higher categories and operads. [3] In the 2010s, he was mainly concerned with a generalization of the Euler characteristic in category theory, the magnitude. He also considered such generalizations in metric spaces with application in biology (measurement of biodiversity).
Exemplar theory is the storage of specific instances (exemplars), with new objects evaluated only with respect to how closely they resemble specific known members (and nonmembers) of the category. This theory hypothesizes that learners store examples verbatim. This theory views concept learning as highly simplistic.
The following outline is provided as an overview of and guide to category theory, the area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows (also called morphisms, although this term also has a specific, non category-theoretical sense), where these collections satisfy certain ...