Information Package / Course Catalogue
Homological Algebra II
Course Code: MTK626
Course Type: Area Elective
Couse Group: Third Cycle (Doctorate Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 8
Objectives of the Course

To introduce advanced homological algebra.

Course Content

To give abstract homological algebra, to study properties of kernels and cokernels, to study arrow categories, to study limit and colimit, to give Lazard’s Theorem, to give dimensions in homology.

Name of Lecturer(s)
Learning Outcomes
1.To introduce advanced homological properties
2.To study some algebraic subjects in homological way
3.To analyse some proof techniques in other fields in homological way
4.To study dimensions in homological way
5.To be able to use mathematical concepts in solving certain types of problems
Recommended or Required Reading
1.Basic Homological Algebra, M. Scott Osborne, Spinger Verlag, 2000.
2.Homology , Saunders Mclane, Spinger Verlag , 1995.
3.Introduction of Homological Algebra, Rotman, J.J., 2009.
4.Relative Homological Algebra, Edgar, E, Enochs, Overtoun M.G. Jenda, Berlin, New York: de Gruyter, 2000.
Weekly Detailed Course Contents
Week 1 - Theoretical
Abstract homological algebra (without elements)
Week 2 - Theoretical
Additive categories
Week 3 - Theoretical
Kernel and cokernel
Week 4 - Theoretical
To study in projectives
Week 5 - Theoretical
Arrow categories
Week 6 - Theoretical
Homologies in abelian categorie
Week 7 - Theoretical
Long exact sequences
Week 8 - Theoretical
A choice for unbalanced categories
Week 9 - Theoretical
Limit and colimit
Week 10 - Theoretical
Adjoint funcktors
Week 11 - Theoretical
Directed colimits, tensor product and Tor
Week 12 - Theoretical
Lazard’s Theorem
Week 13 - Theoretical
Weak dimensions
Week 14 - Theoretical
Injektive envelopes
Assessment Methods and Criteria
Type of AssessmentCountPercent
Assignment2%30
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory143384
Assignment216236
Individual Work140228
Final Examination150252
TOTAL WORKLOAD (hours)200
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
OÇ-1
4
3
4
4
4
4
4
3
3
3
4
4
5
OÇ-2
3
3
4
4
4
4
4
3
3
3
4
4
5
5
OÇ-3
4
4
4
4
4
4
4
4
4
3
4
4
5
5
OÇ-4
4
4
4
4
4
4
4
4
4
3
4
3
4
5
OÇ-5
4
4
4
4
4
4
4
4
5
3
4
4
5
5
Adnan Menderes University - Information Package / Course Catalogue
2026