Title:

Category Theory

Code:TKD
Ac.Year:2017/2018
Term:Winter
Curriculums:
ProgrammeBranchYearDuty
CSE-PHD-4DVI4-Elective
Language:Czech
Completion:examination (written)
Type of
instruction:
Hour/semLecturesSem. ExercisesLab. exercisesComp. exercisesOther
Hours:260000
 ExaminationTestsExercisesLaboratoriesOther
Points:1000000
Guarantee:Šlapal Josef, prof. RNDr., CSc., DADM
Faculty:Faculty of Mechanical Engineering BUT
Department:Department of Algebra and Discrete Mathematics FME BUT
 
Learning objectives:
  The aim of the subject is to make students acquainted with fundamentals of the category theory oriented on applications in computer science. Individual categorical concepts and results are discussed from the view point of their meaning and use in computer science.

 

Description:
  Small and large categories, algebraic structures as categories, constructions on categories (free categories, subcategories and dual categories), special types of objects and morphisms, products and sums of objects, categories with products and circuits, categories with sums and flow charts, distributive categories and imperative programs, data types (arithmetics of reals, stacks, arrays, Binary trees, queues pointers, Turing Machines), functors anf functor categories, directed graphs and regular grammars.

 

 

Knowledge and skills required for the course:
  Basic lectures of mathematics at technical universities
Learning outcomes and competences:
  The students will be acquainted with the fundamental principles of the category theory and with possibilities of applying these principles in computer science. They will be able to use the knowledges gained when solving concrete problems in their specializations.
Syllabus of lectures:
 
  1. Small and large categories
  2. Algebraic structures as categories
  3. Constructions on categories
  4. Properties of objects and morphisms
  5. products and sums of objects
  6. Categories with products and circuits
  7. Categories with sums and flow charts
  8. Distributive categories
  9. Imperative programs
  10. Data types stack, array and binyry tree
  11. Data types queue and pointer, Turing machines
  12. Functors anf functir categories 
  13. Grammars and automata 
Fundamental literature:
 
  • M. Barr, Ch. Wells: Category Theory for Computing Science, Prentice Hall, New York, 1990
  • B.C. Pierce: Basic Category Theory for Computer Scientists, The MIT Press, Cambridge, 1991
  • R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991
Study literature:
 
  • J. Adámek, Mathematical Structures and Categories (in Czech), SNTL, Prague, 1982
  • B.C. Pierce, Basic Category Theory for Computer Scientists, The MIT Press, Cambridge, 1991
  • R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991
Controlled instruction:
  Written essay completing and defending.