Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-49-11-M-6

Categories (M, 3.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-49-11-M-6 Categories 3.0 CP (90 h)

Basedata

CP, Effort 3.0 CP = 90 h
Position of the semester 1 Sem. irreg.
Level [6] Master (General)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-49-11-K-6
Categories
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.


Contents

  • Categories, functors, natural transformations,
  • duality, Yoneda lemma,
  • universal constructions, products, limits,
  • adjoint functors,
  • Abelian categories, kernels, co-kernels, exact sequences.

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.

Literature

  • S. Mac Lane: Categories for the Working Mathematician,
  • H. Schubert: Kategorien I & II.

Requirements for attendance of the module (informal)

Modules:

Courses

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
Module-Pool Name
[MAT-GM-MPOOL-5] General Mathematics (Introductory Modules M.Sc.)