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 appliocations of the categorical language in various areas of computer science, for instance in type theory and in foundations of algebraic specifications.

• Take-home assignement; solutions to be returned by 19 February 2012
• The assignement with a possible solution;

• Universal Algebra (3-24.10)
• Categories (28.20-4.11)
• Limits and colimits (4.11, 7.11, 14.11)
• Factorisation (not ready!)
• Functors and natural transformations (18.11,21.11, ...)
• Adjunctions (5.12, ...)
• Cartesian closed categories (2.01,...)
• Monads (16.01)
• Institutions and some institutional topics

• D.T. Sannella, A. Tarlecki. Foundations of Algebraic Specifications and Formal Program Development. Springer, forthcoming.
  • Chaps 1-4,
  or individual chapters if someone prefers:
  • Chap. 1: Universal algebra
  • Chap. 2: Simple equational specifications
  • Chap. 3: Category theory
  • Chap. 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.

• 2010/11
• 2008/09
• 2005/06
• 2004/05

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