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- Category theory - Wikipedia
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 (mathematics) - Wikipedia
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
- Category Theory - LMU
Category theory provides an answer via the notion of concrete isomorphism Initial structures, final structures, and factorization structures occur in many different situations Category theory allows one to formulate and investigate such concepts with an appropriate degree of generality
- A Gentle Introduction to Categorical Logic and Type Theory
A central idea in category theory is to characterize mathematical constructions by univer-sal properties These are often phrased as existence and uniqueness of certain morphisms making a diagram commute
- Category Theory - Auburn University
Category theory shifts the focus away from the elements of the objects and toward the morphisms between the objects In fact, the axioms of a category do not require that the objects actually be sets, so that in general it does not even make sense to speak of the elements of an object
- Category Theory - Department of Mathematics
Category theory is a general mathematical theory of structures, systems of structures and relationships between systems of structures It provides a unifying and economic mathematical modeling language
- Math 395: Category Theory
Category theory provides a framework through which we can relate a construction fact in one area of mathematics to a construction fact in another The goal is an ultimate form of abstraction, where we can truly single out what about a given problem is specific to that problem, and what is a reflection of a more general phenomenom which appears
- AN INTRODUCTION TO CATEGORY THEORY AND THE YONEDA LEMMA
We provide many examples of each construct and discuss interesting relations between them We proceed to prove the Yoneda Lemma, a central concept in category theory, and motivate its signi cance We conclude with some results and applications of the Yoneda Lemma
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