(in Polish) Teoria toposów i logika kategoryjna 1000-1M20TLK
1. Short review of the basic notions of category theory (representable functors, limits, colomits, adjoint functors).
2. Cartesian, regular, Heyting categories, pretoposes.
3. Elementary toposes - basic properties.
4. Grothendieck toposes - elementary properties related to logic.
5. Theory of monad and Beck theorem.
6. Theories as categories
7. Semantics in toposes.
Type of course
Prerequisites (description)
Learning outcomes
Basic competence in using categories to study logic.
Assessment criteria
Students are expected to present solutions of problems in the class. The exam consists of oral (notions, theorems, proofs) and take home written part (solutions problems). The students particularly active can be exempted from the written part of the exam.
Bibliography
1. Sketches of an Elephant. A Topos Theory Compendium (vol 1 and 2) - Peter Johnstone.
2. Sheaves in Geometry and Logic, S. Mac Lane, I. Moerdijk.
3. Categories for the Working Mathematician, S. Mac Lane.
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:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: