Introduction To Category Theory
Mathematics
Institute of Natural and Applied Sciences
Second Cycle (Master's Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Introduction To Category Theory | MAT534 | Elective | Master's degree | 1 | Spring | 8 |
Name of Lecturer(s)
Prof. Dr. Çiğdem GÜNDÜZ
Associate Prof. Dr. Vildan ÇETKİN
Learning Outcomes of the Course Unit
1) States the notions of object and morphism.
2) Explains the concepts of category and functor.
3) States the Notion of subcategories.
4) States the basic notations and notions in category theory.
5) States the topological categories.
6) Develops categorical viewing skills of topological structures.
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 6 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
topology, algebraic topology
Course Contents
Categories and functors, subcategories, concrete categories and concrete functors, natural transformations, object and morphisms in abstract categories, object and morphisms in concrete categories, topological categories.
Weekly Schedule
1) Fundamental categories and duality principle2) Isomorphisms and properties of functors
3) Categories of categories and object-free definition of categories
4) Subcategories, reflexive and coreflexive subcategories
5) Reflexive and coreflexive subcategories, full subcategories
6) Concrete categories
7) Concrete functors
8) Midterm examination/Assesment
9) Concrete subcategories and transportability
10) Natural transformations and natural isomorphisms
11) Objects and morphisms in abstract categories
12) Objects and morphisms in abstract and concrete categories
13) Objects and morphisms in concrete categories
14) Topological categroies
15) Topological categroies
16) Final examination
Recommended or Required Reading
1- An introduction to Category Theory , H Simmons
2- Category Theory, Steve Awodey
3- Algebra, Topology, and Category Theory, ALEX HELLER and MYLES TIERNEY
Planned Learning Activities and Teaching Methods
1) Lecture
2) Question-Answer
3) Discussion
4) Drill and Practice
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
40% |
|---|---|
Contribution of Final Examination to Course Grade |
60% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required