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Lecturer(s)
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Šlapal Josef, prof. RNDr. CSc.
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Bělohlávek Radim, prof. RNDr. Ph.D., DSc.
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Course content
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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. 1. Graphs and categories 2. Algebraic structures as categories 3. Constructions on categories 4. Properties of objects and morphisms 5. Products and sums of objects 6. Natural numbers objects and deduction systems 7. Functors and diagrams 8. Functor categories, grammars and automata 9. Natural transformations 10. Limits and colimits 11. Adjoint functors 12. Cartesian closed categories and typed lambda-calculus 13. The cartesian closed category of Scott domains
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Learning activities and teaching methods
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Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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The students will be acquainted with the fundamental principles of the category theory and with possibilities of applying these principles to computer science.
1. Knowledge Describe and understand comprehensively principles and methods of category theory.
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Prerequisites
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unspecified
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Assessment methods and criteria
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Oral exam
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Recommended literature
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Adámek. (1982). Matematické struktury a kategorie. SNTL, Praha.
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Barr M., Wells Ch. (1999). Category Theory for Computing Science. Prentice Hall, New York.
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Pierce B. C. (1991). Basic Category Theory for Computer Scientists. The MIT Press, Cambridge.
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Walters R. F. C. (1991). Categories and Computer Science. Cambridge Univ. Press.
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