FI:M027 Teorie kategorií - Course Information

M027 Teorie kategorií

Extent and Intensity

2/0. 2 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).

Teacher(s)

prof. RNDr. Jiří Rosický, DrSc. (lecturer)

Guaranteed by

Contact Person: prof. RNDr. Jiří Rosický, DrSc.

Prerequisites

Before enrolling this course the students should go through M005 Foundations of mathematics, M003 Linear Algebra and Geometry I, M004 Linear Algebra and Geometry II, M008 Algebra I, M009 Algebra II, M006 Set Theory and M007 Mathematical Logic.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Informatics (programme FI, B-IN)
• Informatics (programme FI, M-IN)
• Upper Secondary School Teacher Training in Informatics (programme FI, M-IN)
• Upper Secondary School Teacher Training in Informatics (programme FI, M-SS)
• Information Technology (programme FI, B-IN)

Syllabus

• Categories: category, constructions of categories, special objects and morphisms
• Products and sums
• Functors: functor, diagram
• Natural transformations: natural transformation, Yoneda lemma, representable functors
• Cartesian closed categories
• Limits: equalizer, pullback, limit, colimit, limits by products and equalizers
• Adjoint functors: adjoint functor, Freyd's theorem
• Closed categories: monoidal category, symmetric monoidal closed category, connection with linear logic

Language of instruction

Czech

• Enrolment Statistics (Autumn 1996, recent)
  
• Permalink: https://is.muni.cz/course/fi/autumn1996/M027