TÜRKÇE
ENGLISH
Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| MATHEMATICS (MASTER) (WITH THESIS) | |
| Code | MT576 |
| Name | Category Theory |
| Term | 2025-2026 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. YILMAZ DURĞUN |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
By the end of this course, students will understand the fundamental principles of category theory, be able to analyze various mathematical structures and relationships through category theory, and apply this knowledge in different mathematical fields.
Course Content
Foundations of Category Theory, Basic Properties of Categories, Functors (Functional Structures), Natural Transformations, Relationships Between Categories, Kernels and Categorical Kernels, Limits and Colimits, Finite Limits, Infinite Limits, Monoids and Group Categories, Abelian Categories, Categorical Geometry, Categories and Topological Spaces.
Course Precondition
None
Resources
Mac Lane, S. (1971). Categories for the Working Mathematician (Graduate Texts in Mathematics). Awodey, S. (2010). Category Theory (Oxford Logic Guides).
Notes
Borceux, F. (1994). Handbook of Categorical Algebra Vol. 1, 2, and 3 (Encyclopedia of Mathematics and its Applications).
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learns the relationship between categories, objects, and morphisms. |
| LO02 | Understand the role of category theory in the study of mathematical structures. |
| LO03 | Learn about functors and natural transformations. |
| LO04 | They learn the structural aspects of category theory. |
| LO05 | Understands interactions between categories. |
| LO06 | Explores abstract connections between mathematical structures through category theory. |
| LO07 | Can integrate mathematical concepts from different fields through category theory. |
| LO08 | They learn to construct logical arguments. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | 5 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | 3 |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | 4 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Foundations of Category Theory | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Basic Properties of Categories | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Functors-1 | Required reading | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Functors-2 | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Natural Transformations | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Relationships Between Categories | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Kernels and Categorical Kernels | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Required readings | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Limits | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Colimits | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Finite Limits | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Infinite Limits | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Monoids and Group Categories | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Abelian Categories | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Categorical Geometry | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Required readings | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Required readings | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||