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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 is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. [1] Category theory is used in almost all areas of mathematics.
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 ...
Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical computer science. [1] In broad terms, categorical logic represents both syntax and semantics by a category, and an interpretation by a functor.
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 ...
Cosmoses which categorize universes: A cosmos is a generalized universe of 1-categories in which you can do category theory. When set theory is generalized to the study of a Grothendieck topos, the analogous generalization of category theory is the study of a cosmos. Ross Street definition: A bicategory such that; small bicoproducts exist;
Download as PDF; Printable version; ... Category theory is a mathematical theory that deals in an abstract way with mathematical ... Free algebraic structures (25 P ...