(in Polish) Teoria toposów i logika kategoryjna

General data

Course ID:	1000-1M20TLK
Erasmus code / ISCED:	11.1 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	(unknown)
Name in Polish:	Teoria toposów i logika kategoryjna
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective monographs
Prerequisites (description):	Participants are expected to have a general mathematical background nor exceeding first two years of math curriculum, as well as basic acquittance with category theory not exceeding a half a year course in category theory.
Short description:	It is an introduction to categorical logic, i.e. studies of logic using categories both on the syntactic side (cartesian categories, regular categories, pretoposes) and on semantic side (elementary toposes, Grothendieck toposes).
Full description:	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.
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.
Learning outcomes:	Basic competence in using categories to study logic.
Assessment methods and 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.

This course is not currently offered.

Course descriptions are protected by copyright.
Copyright by University of Warsaw.