Course detail
Basics of Category Theory
FSI-9TKD Acad. year: 2024/2025 Winter semester
The aim of the subject is to make students acquainted with basic concepts and results of category theory with respect to their applications in various fields, particularly in computer science. They will be able to use the knowledge acquainted in their professional specializations.
Language of instruction
Czech
Supervisor
Department
Entry knowledge
The knowledge is expected of the subjects General Algebra and Methods of discrete mathematics taught within the Bachelor's level and Graph theory and Mathematical structures taught within the Master's level of the study programme mathematical Engineering.
Rules for evaluation and completion of the course
Students are to pass an exam consisting of the written and oral parts. During the exam, their knowledge of the concepts introduced and of the basic propertief of these concepts will be assessed. Also their ability to use theoretic results for solving concrete problems will be evaluated.
Since the subject is taught in the form of a lecture, which is not compulsory for student, the attendance will not be checked.
Aims
The goal of the subject is to get students acquainted with basics of the category theory and some of its applications in computer science.
Students will get basic knowledge of the category theory and will learn using them for solving some problems of computer science like creating logic circuits and flow charts.
The study programmes with the given course
Programme D-APM-K: Applied Mathematics, Doctoral, recommended course
Programme D-APM-P: Applied Mathematics, Doctoral, recommended course
Type of course unit
Lecture
20 hours, optionally
Syllabus
1. Graphs and categories
2. Algebraic structures as categories
3. Constructions on categories
4. Properties of objects and morphisms
5. Products and sums of objects
6. Natural numbers objects and deduction systems
7. Functors and diagrams
8. Functor categories, grammars and automata
9. Natural transformations
10.Limits and colimits
11.Adjoint functors
12.Cartesian closed categories and typed lambda-calculus
13.The cartesian closed category of Scott domains