- Categories, functors, natural transformations,
- duality, Yoneda lemma,
- universal constructions, products, limits,
- adjoint functors,
- Abelian categories, kernels, co-kernels, exact sequences.
Categories (M, 3.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-49-11-M-6||Categories||3.0 CP (90 h)|
|CP, Effort||3.0 CP = 90 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (General)|
|Area of study||[MAT-AGCA] Algebra, Geometry and Computer Algebra|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
|P||28 h||62 h||-||-||PL1||3.0||irreg.|
- About [MAT-49-11-K-6]: Title: "Categories"; Presence-Time: 28 h; Self-Study: 62 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: irregular (by arrangement)
- Examination number: 84152 ("Categories")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
Upon successful completion of this module, the students have studied the fundamental formal structures that serve as a basis for many areas of mathematics. They have deepened their abilities of methodical abstraction. With the help of examples from different areas of mathematics, they have trained themselves to identify equivalent structures in different contexts. They understand the proofs presented in the lecture and are able to comprehend and explain them.
- S. Mac Lane: Categories for the Working Mathematician,
- H. Schubert: Kategorien I & II.
Requirements for attendance of the module (informal)
Requirements for attendance of the module (formal)None
References to Module / Module Number [MAT-49-11-M-6]
|Course of Study||Section||Choice/Obligation|
|[MAT-88.105-SG] M.Sc. Mathematics||[Core Modules (non specialised)] Pure Mathematics||[WP] Compulsory Elective|
|[MAT-88.706-SG] M.Sc. Mathematics International||[Core Modules (non specialised)] Pure Mathematics||[WP] Compulsory Elective|
|[MAT-GM-MPOOL-5]||General Mathematics (Introductory Modules M.Sc.)|