Recent developments in mathematics have in a sense organized objects of study into categories, where properties of mathematical systems can be unified and simplified through presentation of diagrams with arrows. A cat...Recent developments in mathematics have in a sense organized objects of study into categories, where properties of mathematical systems can be unified and simplified through presentation of diagrams with arrows. A category is an algebraic structure made up of a collection of objects linked together by morphisms. Category theory has been advanced as a more concrete foundation of mathematics as opposed to set-theoretic language. In this paper, we define a pseudo-category on the class of isotonic spaces on which the idempotent axiom of the Kuratowski closure operator is assumed.展开更多
A typed category theory is proposed for the abstract description of knowledge and knowledge processing. It differs from the traditional category theory in two directions： all morphisms have types and the composition ...A typed category theory is proposed for the abstract description of knowledge and knowledge processing. It differs from the traditional category theory in two directions： all morphisms have types and the composition of morphisms is not necessary a morphism. Two aspects of application of typed category theory are discussed： cones and limits of knowledge complexity classes and knowledge completion with pseudo-functors.展开更多
文摘Recent developments in mathematics have in a sense organized objects of study into categories, where properties of mathematical systems can be unified and simplified through presentation of diagrams with arrows. A category is an algebraic structure made up of a collection of objects linked together by morphisms. Category theory has been advanced as a more concrete foundation of mathematics as opposed to set-theoretic language. In this paper, we define a pseudo-category on the class of isotonic spaces on which the idempotent axiom of the Kuratowski closure operator is assumed.
文摘A typed category theory is proposed for the abstract description of knowledge and knowledge processing. It differs from the traditional category theory in two directions： all morphisms have types and the composition of morphisms is not necessary a morphism. Two aspects of application of typed category theory are discussed： cones and limits of knowledge complexity classes and knowledge completion with pseudo-functors.
