Fundamentals of Category Theory - NMAT001

• Title: Základy teorie kategorií
• Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2018
• 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: cancelled
• Language: Czech
• Teaching methods: full-time
• Teaching methods: full-time
• Guarantor: doc. RNDr. Petr Somberg, Ph.D.
• Classification: Mathematics > Topology and Category
• Interchangeability : NMAG471
• Is incompatible with: NMAG441, NMAG471
• Is interchangeable with: NMAG471, NMAG441

Annotation

English

Last update: T_MUUK (18.12.2000)

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: ()

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

Literature

Last update: RNDr. Pavel Zakouřil, Ph.D. (05.08.2002)

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

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

Syllabus

English

Last update: T_MUUK (20.05.2004)

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: ()

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.