Introduction to Category Theory

MATH X 451.45

This course is an introduction to the basic tenets of category theory, as formulated and illustrated through examples drawn from algebra, calculus, geometry, set theory, topology, number theory, and linear algebra.

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What you can learn.

  • Explore mathematical category theories that are applied in computer science
  • Analyze the various relationships between vectors
  • Apply the concepts from algebra, calculus and geometry in the field of computer science
  • Learn how abstract mathematical concepts can be utilized in solving computer vector spaces

About this course:

Category theory, since its development in the 1940s, has assumed an increasingly center-stage role in formalizing mathematics and providing tools to diverse scientific disciplines, most notably computer science. A category is fundamentally a family of mathematical obejcts (e.g., numbers, vector spaces, groups, topological spaces) along with “mappings” (so-called morphisms) between these objects that, in some defined sense, preserve structure. Taking it one step further, one can consider morphisms (so-called functors) between categories. This course is an introduction to the basic tenets of category theory, as formulated and illustrated through examples drawn from algebra, calculus, geometry, set theory, topology, number theory, and linear algebra. Topics to be discussed include: isomorphism; products and coproducts; dual categories; covariant, contravariant, and adjoint functors; abelian and additive categories; and the Yoneda Lemma. The course should appeal to devotees of mathematical reasoning, computer scientists, and those wishing to gain basic insights into a hot area of mathematics.
Suggested Prerequisites

It is advisable that you complete the following (or equivalent) since they are prerequisites for Introduction to Category Theory.

Prerequisites: Some exposure to advanced mathematical methods from algebra and geometry.

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