Introduction
Category theory is a branch of mathematics that studies the abstract patterns and structures that appear in different mathematical domains. It focuses on the relationships between objects and the transformations that preserve their properties. Category theory can be used to unify and generalize concepts from various fields of mathematics, such as algebra, topology, logic, and computation.
Content
Basic of Categories
Structure of Categories
Objects and Elements
Morphisms
Functoriality and Naturality
Constructions on Categories
Free Categories
Constructions on Objects
Products of Objects
Equalizers and Coequalizers
Pullback and Pushout
Limits and Colimits
Exponential
Groups and Categories
Monoidal Categories
Abelian Categories
Naturality and Yoneda
Higher Categories ^f2a96d
Specific Categories
Finite Sets Category
Finite Category
Relation Category
Posets Category
Preorder Category
Logic Category
More …
Group Theory
Ring Theory
Categorical Quantum Mechanics
Lambda Calculus
Actegories
Other Resources
Acknowledgement
This part is mainly based on the ANU ASC SCNC3101 in 2024, supervised by Dr Ranald Clouston.