Title:  Category Theory 

Code:  TKD 

Ac.Year:  2008/2009 

Term:  Summer 

Curriculums:  

Language:  Czech 

Completion:  examination (written) 

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

Hours:  39  0  0  0  0 

 Examination  Tests  Exercises  Laboratories  Other 

Points:  0  0  0  0  0 



Guarantee:  Šlapal Josef, prof. RNDr., CSc., DADM 

Lecturer:  Šlapal Josef, prof. RNDr., CSc., DADM 
Faculty:  Faculty of Information Technology BUT 

 Learning objectives: 

  The aim of the subject is to make students acquainted with fundamentals of the category theory with respect to applications to computer science. Some important concrete applications will be discussed in greater detail.  Description: 

  Graphs and categories, algebraic structures as categories, constructions on categories (subcategories and dual categories), special types of objects and morphisms, products and sums of objects, natural numbers objects, deduction systems, functors and diagrams, functor categories, grammars and automata, natural transformations, limits and colimits, adjoint functors, cartesian closed categories and typed lambdacalculus, the cartesian closed category of Scott domains.  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 to computer science. They will be able to use the knowledges gained when solving concrete problems in their specializations.  Syllabus of lectures: 


 Graphs and categories
 Algebraic structures as categories
 Constructions on categories
 Properties of objects and morphisms
 Products and sums of objects
 Natural numbers objects and deduction systems
 Functors and diagrams
 Functor categories, grammars and automata
 Natural transformations
 Limits and colimits
 Adjoint functors
 Cartesian closed categories and typed lambdacalculus
 The cartesian closed category of Scott domains
 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.  
