The course recalls basic concepts of universal algebra and introduces the language of category theory, limited to the most elementary and important notions and related results. We hint at least at the possible applications of the categorical language in various areas of computer science, for instance in type theory and in foundations of algebraic specifications.

• old compact version, subject to modification and expansion:
  • Universal Algebra
  • Categories
  • Limits and colimits
  • Factorisation (not ready!)
  • Functors and natural transformations
  • Adjunctions
  • Cartesian closed categories
  • Monads
  • Institutions and some institutional topics
• The above are better for printing (but contain minor inaccuracies); the actual course will use their corrected and expanded version, with overlays, as given below (minor corrections still possible where the dates are not given):
  • Preliminaries (4/10)
  • Universal Algebra (4,11,18,25/10)
  • Categories (25/10, 8/11)
  • Limits (15/11)
  • Functors (22,29/11)
  • Natural transformations (6/12)
  • Adjunctions (13,20/12, 10/01)
  • Cartesian closed categories (17/01)
  • Monads (24/01)
  • Institutions

• D.T. Sannella, A. Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Springer, 2012.
  Initial chapters, containing most of the material in this course, in a pre-publication version:
  • Chapters 1-4; or if someone prefers them one by one:
    • Chapter 1 (universal algebra)
    • Chapter 2 (equational specifications)
    • Chapter 3 (basic category theory)
    • Chapter 4 (institutions)
• plenty of classical monographs on universal algebra, like:
  • George A. Graetzer. Universal Algebra. Springer, second edition, 1979.
  and category theory, like:
  • Saunders MacLane. Categories for the Working Mathematician. Springer, 1971.

Exam:

Here are a few samples of exam assignments from the past (sorry, only some English versions are available):

• 2023/24
• 2022/23
• 2021/22
• 2020/21
• 2019/20

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