6 ECTS credits
150 h study time
Offer 1 with catalog number 4013385FNR for all students in the 2nd semester
at
a (F) Master - specialised level.
- Semester
- 2nd semester
- Enrollment based on exam contract
- Impossible
- Grading method
- Grading (scale from 0 to 20)
- Can retake in second session
- Yes
- Taught in
- Dutch
- Faculty
- Faculty of Science and Bio-engineering Sciences
- Department
- Mathematics
- Educational team
- Ana Agore
(course titular)
- Activities and contact hours
-
30 contact hours Lecture
30 contact hours Seminar, Exercises or Practicals
- Course Content
- Basic notions:
Categories, Functors and Natural Transformations, Representable functors, The Yoneda Lemma.
Special objects and morphisms in a category:
Monomorphism, Epimorphism, Isomorphism, Initial object, Terminal object, Zero-object.
Constructions:
Dual category, Product of categories, Functorcategory, Commacategory, Free category on a graph.
(Co)limits:
(Co)products, (Co)equalizers, Pullbacks, Pushouts, (Co)limit of a functor, (Co)complete
categories, Limit-preserving functors.
Adjoint functors:
Adjointness of functors, Equivalence of categories, (Co)reflective subcategories, Localization of a category, Freyd's adjoint functor theorem, Kan extensions.
Monads and algebras.
- Course material
- Digital course material (Required) : Categorietheorie, Nota's van de titularis zijn beschikbaar
Handbook (Recommended) : Categories for the working mathematician, S. MAC LANE, Second Edition, Springer, 9781441931238, 1978
Handbook (Recommended) : Handbook of categorical algebra 1, F. BORCEUX, Cambridge University Press, 9780521061193, 2008
Handbook (Recommended) : Abstract and concrete categories, J. ADAMEK, H. HERRLICH and G. STRECKER, Wiley, 9780486469348, 2009
- Additional info
- If necessary, the course will be taught in English. Copies of course notes are available.
Complementary study material:
Literature (available in the library):
J. ADAMEK, H. HERRLICH and G. STRECKER, Abstract and concrete categories, Wiley 1990
F. BORCEUX, Handbook of categorical algebra 1, Cambridge University Press 1994
S. MAC LANE, Categories for the working mathematician, Springer 1971 and Springer 1998 (2nd Edition)
- Learning Outcomes
-
General competencies
The aim of this course is the study of the basic notions of category theory,
their universality in mathematics being illustrated by various concrete examples
from analysis, algebra and topology and from relations between these fields.
Students will learn to work with these notions by solving illuminating exercises,
they will get the feeling for categorical proofs and they will appreciate the strength
of categorical statements.
- Grading
-
The final grade is composed based on the following categories:
Oral Exam determines 70% of the final mark.
Written Exam determines 30% of the final mark.
Within the Oral Exam category, the following assignments need to be completed:
- Mondeling theorie examen
with a relative weight of 1
which comprises 70% of the final mark.
Within the Written Exam category, the following assignments need to be completed:
- Schriftelijk oefeningen examen
with a relative weight of 1
which comprises 30% of the final mark.
- Additional info regarding evaluation
- Theory: Oral exam (counting for 70%)
Exercises: Written exam (counting for 30%)
- Allowed unsatisfactory mark
- The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.
Academic context
This offer is part of the following study plans:
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)