Title:  Category Theory 

Code:  TKD 

Ac.Year:  2017/2018 

Term:  Winter 

Curriculums:  

Language:  Czech 

Completion:  examination (written) 

Type of instruction:  Hour/sem  Lectures  Sem. Exercises  Lab. exercises  Comp. exercises  Other 

Hours:  26  0  0  0  0 

 Examination  Tests  Exercises  Laboratories  Other 

Points:  100  0  0  0  0 



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: 

  Small and large categories
 Algebraic structures as categories
 Constructions on categories
 Properties of objects and morphisms
 products and sums of objects
 Categories with products and circuits
 Categories with sums and flow charts
 Distributive categories
 Imperative programs
 Data types stack, array and binyry tree
 Data types queue and pointer, Turing machines
 Functors anf functir categories
 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.  
