Category theory is used to formalize mathematics and its concepts as a collection of objects and arrows (also called morphisms). Category theory can be used to formalize concepts of other high-level abstractions such as set theory, ring theory, and group theory. Several terms used in category theory, including the term "morphism", differ from their uses within mathematics itself. In category theory, a "morphism" obeys a set of conditions specific to category theory itself. Thus, care must be taken to understand the context in which statements are made.
Category Theory is utilized where abstractions are categories and scopes are morphisms. Connections between abstractions are also morphisms.
Abstractions can be considered categories. Abstractions can be connected by a morphism. Abstractions can also be learned (a morphism).
The structure of the definitions in this philosophy are nested categories.
The sub-sections:
- Cultural Definition
- This Philosophy Definition
And subsections of the subsections are also categories.
Cultural Definition
(mathematics) A branch of mathematics which deals with spaces and maps between them in abstraction, taking similar theorems from various disparate more concrete branches of mathematics and unifying them.
Category theory is used to formalize mathematics and its concepts as a collection of objects and arrows (also called morphisms). Category theory can be used to formalize concepts of other high-level abstractions such as set theory, ring theory, and group theory. Several terms used in category theory, including the term "morphism", differ from their uses within mathematics itself. In category theory, a "morphism" obeys a set of conditions specific to category theory itself. Thus, care must be taken to understand the context in which statements are made.
Category Theory by Tom LaGatta (youtube.com)
Introduction to Category Theory - Graham Hutton
Pattern Expression
Category Theory applies to all abstractions.