Fundamentals of Category Theory - NMAG471

• Title: Základy teorie kategorií
• Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2020
• Semester: winter
• E-Credits: 6
• Hours per week, examination: winter s.:2/2, C+Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Teaching methods: full-time
• Guarantor: Dr. Re O'Buachalla, Dr.
• Class: M Mgr. MSTR; M Mgr. MSTR > Volitelné
• Classification: Mathematics > Topology and Category
• Incompatibility : NMAT001
• Interchangeability : NMAT001
• Is interchangeable with: NMAT001

Annotation

English

Last update: T_MUUK (06.05.2015)

Introductory course on category theory.

Czech

Last update: G_M (24.05.2013)

Úvodní přednáška z teorie kategorií, na kterou navazují další přednášky.

Course completion requirements

English

Last update: Mgr. Dalibor Šmíd, Ph.D. (28.10.2019)

There will be several homeworks. As a requirement to take the final exam students must submit

solutions to at least one homework. The final exam will be an oral exam.

Czech

Last update: Mgr. Dalibor Šmíd, Ph.D. (28.10.2019)

K zápočtu je třeba alespoň jeden domácí úkol, zkouška je ústní, zápočet je podmínkou zkoušky.

Literature

English

Last update: Roman Golovko, Ph.D. (26.09.2018)

1) T. Leinster: Basic Category Theory, Cambridge Studies in Advanced Mathematics 143, Cam-

bridge University Press, 2014. Available at arXiv:1612.09375.

2) S. MacLane: Categories for the Working Mathematician, Springer Verlag, Berlin, 1971

3) J. Adamek, H. Herrlich, G. Strecker: Abstract and Concrete Categories , John Wiley, New

York, 1990

Czech

Last update: Roman Golovko, Ph.D. (26.09.2018)

1) T. Leinster: Basic Category Theory, Cambridge Studies in Advanced Mathematics 143, Cam-

bridge University Press, 2014. Available at arXiv:1612.09375.

2) S. MacLane: Categories for the Working Mathematician , Springer Verlag, Berlin, 1971

3) J. Adámek, H. Herrlich, G. Strecker: Abstract and Concrete Categories , John Wiley, New York, 1990

Requirements to the exam

English

Last update: Roman Golovko, Ph.D. (26.09.2018)

There will be several homeworks. As a requirement to take the final exam students must submit

solutions to at least one homework. The final exam will be an oral exam.

Czech

Last update: Roman Golovko, Ph.D. (26.09.2018)

Bude zadáno několik domácích úkolů. Podmínkou k zápočtu je odevzdání alespoň jednoho správného řešení.

Zkouška má ústní formu.

Syllabus

English

Last update: Roman Golovko, Ph.D. (26.09.2018)

The basic notions and facts of category theory are presented, namely

category and subcategory, covariant and contravariant functors, full

and faithful, hom-functors, natural transfomations and the functor

categories, Yoneda lemma; limits and colimits of diagrams, Maranda's

and Mitchel's theorems; adjoint functors, free functors, reflective

and coreflective subcategories, closed and Cartesian closed categories,

contravariant adjoints and dualities; comma-categories; Adjoint Functor

Theorem and Special Adjoint Functor Theorem; extremal and regular

monomorphisms (epimorphisms), factorization systems.

For all the above, many examples and some applications are given.

Czech

Last update: Roman Golovko, Ph.D. (26.09.2018)

Základní kurs z teorie kategorií pro směr Matematické struktury. Přednáška seznamuje se základními pojmy a větami.

1) Pojem kategorie, funktoru, přirozené transformace, kategorie malé a konkretizovatelné.

2) Diagramy, jejich limity a kolimity, Marandova věta, zachovávání limit a kolimit.

3) Kategorie funktorů, Yonedovo lemma a Yonedovo vnoření, použití.

4) Adjunkty, věty o adjunktech, použití.