Category theory in foundations of computer science 1000-2M10TKI
Plan:
Many-sorted sets, basic notions and notationf of set theory.
Many-sorted algebras, basic algebraic concepts.
Terms, equations, equational varieties; equational calculus.
Initial algebras, algebraic specifications with initial semantics.
Related algebraic frameworks.
Categories and basic catoegorical concepts.
Limits and colimits.
Functors and natural transformations.
Adjunctions.
Monads and algebras.
Cartesian-closed categories and semantics of typed lambda calculus.
Type of course
Mode
Course coordinators
Assessment criteria
Written take-home exam, marked by the lecturer, likely to take the form of a larger assignment with multiple subtasks.
If the exam is needed earlier, please contact the lecturer.
There will be a special subtask or a separate assignment at a more advanced level for PhD students taking the exam.
Bibliography
G. Graetzer, Universla Algebra, Springer, 1979.
S. MacLane, Categories for the Working Mathematician, Springer, 1971
D.T. Sannella, A. Tarlecki, Foundations of Algebraic Specificiations and Formal Program Development, Springer, 2012.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
- Bachelor's degree, first cycle programme, Computer Science
- Master's degree, second cycle programme, Computer Science
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: