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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 ...
Categories for the Working Mathematician (CWM) is a textbook in category theory written by American mathematician Saunders Mac Lane, who cofounded the subject together with Samuel Eilenberg. It was first published in 1971, and is based on his lectures on the subject given at the University of Chicago , the Australian National University ...
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 ]
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 ...
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).
Monads in category theory (then called standard constructions and triples). Monads generalize classical notions from universal algebra and can in this sense be thought of as an algebraic theory over a category: the theory of the category of T-algebras. An algebra for a monad subsumes and generalizes the notion of a model for an algebraic theory.