Course Unit


Mathematical Structures

  • Unit Coordinator: Josef Šlapal
  • Programme: Double Degrees
  • ECTS Credits: 4
  • Semester: 2
  • Year: 2
  • Campus: Brno University of Technology
  • Aims:

    The aim of the course is to show the students possibility of a unified perspective on seemingly different mathematical subjects.

  • Content:

    1. Sets and classes

    2. Mathematical structures

    3. Isomorphisms

    4. Fibres

    5. Subobjects

    6. Quotient objects

    7. Free objects

    8. Initial structures

    9. Final structures

    10. Cartesian product

    11. Cartesian completeness

    12. Functors

    13. Relection and corelection

  • Pre-requisites:

    Students are expected to know the mathematics taught within the bachelor's study programme and the graph theory taught in the master's study

  • Reading list:
    •  Jiří Adámek, Theory of Mathematical Structures, D. Reidel Publ. Company, Dordrecht, 1983.
    • A.Adámek, H.Herrlich. G.E.Strecker: Abstract and Concrete Categories, John Willey & Sons, New York, 1990
  • Additional info:

    The course will familiarise students with basic concepts and results of the theory of mathematical structures. A number of examples of concrete structures will be used to demonstrate the exposition.


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