INTRODUCTION TO CATEGORY THEORY

Course General Information

Course Code ECTS T+A+L Credit Type of Course Unit
MAT20742 7 3+0 3 Elective
Course Link (Turkish) :
Course Link (English) :
Language of Instruction Turkish
Level of Course Unit Graduate
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course The aim of this course is to give an introductory account of the categories with some applications.
Course Content Introduction, Categories, Functors, Natural Transformations, Constructions on Categories, Universals and Limits.
Prerequisites and co-requisities None
Course Coordinator Matematik Anabilim Dalı Başkanlığı
Name of Lecturers Dr. Öğr. Üyesi Ramazan EKMEKÇİ
Assistants Yok
Work Placement(s) No

Recommended or Required Reading

Resources 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
Notes None
Preparation and Documentation None
Home Work None

Course Category

Mathematics and Basic Sciences% 100
Engineering% 0
Engineering Design% 0
Social Sciences% 0
Education% 0
Science% 0
Health% 0
Field% 0
Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Mid-terms 1 % 40
Quizzes 0 % 0
Assignment 0 % 0
Attendance 0 % 0
Practice 0 % 0
Project 0 % 0
Final examination 1 % 60
Field Work 0 % 0
Workshop 0 % 0
Laboratory 0 % 0
Preparation of Presentation/Seminar 0 % 0
Total 2 % 100
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Course Duration 14 3 42
Hours for off-the-c.r.stud 14 11 154
Assignments 0 0 0
Mid-terms 1 3 3
Final examination 1 3 3
Quizzes 0 0 0
  202 | AKTS Kredisi : 7

Weekly Detailed Course Contents

Week Topic Teaching Methods and Techniques Preparation and Documentation
1 Definition of Categories, Concept of Cartesian Product, Concept of Adjoint, Concept of Functor, Monoids. Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
2 Axioms for Categories, Examples of Category. Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
3 Examples of Functor, Natural Transformations. Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
4 Monics, Epis and Zeros, Foundations, Some Large Categories. Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
5 Hom-sets, Constructions on Categories, Duality, Contravariance and Opposites. Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
6 Products of Categories. Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
7 Functor Categories, Examples, Double Category. Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
8 Midterm Exam None None
9 Double Category (continue), Comma Categories. Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
10 Graphs and Free Categories, Quotient Categories. Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
11 Universals and Limits. Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
12 Coproducts and Colimits, Copowers, Cokernels, Coequalizers. Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
13 Pushouts, Cokernel Pairs, Colimits, Limits Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
14 Products, Infinite Products and Powers, Equalizers, Pullbacks. Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.
15 Final preparation Lecturing, question-answer, discussion, problem solving. 1. Abstract and Concrete Categories; J. Adamek, H. Herrlich, G. E. Strecker.2. Saunders Mac Lane, Categories for the Working Mathematician, Springer, 1971.

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:

# Learning Outcomes
1 Infers the basic concepts and methods of categories.
2 Interprets how category theory can be used to structure mathematical ideas, with the concepts of functoriality, naturality and universality.
3 Detects how reasoning with objects and arrows can replace reasoning with sets and elements.
4 Infers the basic ideas of using commutative diagrams and unique existence properties.
5 Infers the connections between categories and logic.

Contribution of Learning Outcomes to Programme Outcomes

  P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12
C1 554455434454
C2 454544434555
C3 554545434545
C4 544554534455
C5 454545445454

Contribution: 1:Very Slight     2:Slight     3:Moderate     4:Significant     5:Very Significant