Search results
Results from the WOW.Com Content Network
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.
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 ]
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.
Category theory is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas ...
Categories help the reasoner to render signs ready for the application of logical laws. An equivocation is a variation in meaning—a manifold of sign senses—such that, as Aristotle put it about names in the opening of Categories (1.1 a 1–12), "Things are said to be named 'equivocally' when, though they have a common name, the definition ...
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 ...
The notion of exact sequence is meaningful in Grp, and some results from the theory of abelian categories, such as the nine lemma, the five lemma, and their consequences hold true in Grp. The snake lemma however is not true in Grp. [dubious – discuss] [citation needed] Grp is a regular category.
The interpretation of the logic is that in every class category the universe is a model of basic intuitionistic set theory (BIST) that is logically complete with respect to class category models. Therefore, class categories generalize both topos theory and intuitionistic set theory.