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Elements of Category Theory

General data

Course ID:	1000-1M07ET
Erasmus code / ISCED:	11.114 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:	Elements of Category Theory
Name in Polish:	Elementy teorii kategorii
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):	6.00 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
Short description:	Basic notions and theorems of Category Theory will be discussed. Some specific applications will be covered in the last part of the course. I intend to discuss various aspects of Grothendieck topoi.
Full description:	Most of the lecture will be an introduction to Category Theory, covering the following notions and theorems: categories, functors, natural transformations, equivalence of categories, representable functors, The Yoneda Lemma, limits, colimits, adjoint functors, GAFT, SAFT, cartesian closed categories, presheaf categories, monads, Eilenberg-Moore and Kleisli algebras, Beck's Theorem. The lecture will be illustrated by examples taken mostly from algebra, topology and logic. In the remaining part of the lecture I intend to discuss Grothendieck toposes from various points of view: as generalized topological spaces, universes of 'sets', and geometric theories. The participants' interests may substantially influence the choice of the material covered in this part. The course will end with a written exam.
Bibliography:	General introduction: S. MacLane, Categories for the Working Mathematician, M. Barr, Ch. Wells, Category Theory for Computing Science Topos Theory: I. Moerdijk, S. MacLane, Sheaves in Geometry and Logic M. Barr, Ch. Wells, Toposes, Triples and Theories Handbooks: P. T. Johnstone, Sketches of an Elephant: A Topos Theory Compendium F. Borceux, Handbook of Categorical Algebra
Assessment methods and assessment criteria:	The grading will be made on the basis of 1. Active participation in class 2. Written solutions of a set of problems 3. Oral exam

Classes in period "Winter semester 2023/24" (past)

Time span:	2023-10-01 - 2024-01-28	Selected timetable range: weekly course term Navigate to timetable MO TU W WYK-MON CW TH FR
Type of class:	Classes, 30 hours more information Monographic lecture, 30 hours more information
Coordinators:	Marek Zawadowski
Group instructors:	Wojciech Duliński, Marek Zawadowski
Students list:	(inaccessible to you)
Examination:	Examination

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