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Non-repeated universal elective course.
In the academic year 2025/26: Introduction to infinity categories (Sebastian Opper).
The course offers an introductory account to the theory of infinity categories. This a very flexible generalisation of
classical category theory which has become an increasingly important and powerful framework for many areas
such as topology, homotopy theory, algebra and algebraic geometry.
Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (09.09.2025)
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The exam will be oral. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (30.09.2024)
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(1) ’∞-categories: a first course’. Lecture notes by Martin Gallauer, available online at https://mgallauer.warwick.ac.uk/teaching/23icats/icats.pdf (2) ’Higher categories and homotopical algebra’, Cambridge University Press. Book by Denis-Charles Cisinksi, available at author’s homepage: https://cisinski.app.uniregensburg.de/CatLR.pdf (3) Kerodon: searchable online resource for homotopy coherent mathematics. Maintained by Jacob Lurie at https://kerodon.net/ Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (10.09.2025)
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The course is completed with an oral exam. The requirements for the exam correspond to what is presented in lectures. Last update: STOVJ8AM (11.10.2017)
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The course offers an introductory account to the theory of infinity categories. This a very flexible generalisation of classical category theory which has become an increasingly important and powerful framework for many areas such as topology, homotopy theory, algebra and algebraic geometry. Outlook: (1) Review of simplicial sets, nerve-realisation adjunctions; ordinary categories and topological spaces as ∞-categories (2) Discussion of ∞-categorical versions of concepts such as (co)limits and the Yoneda embedding. (3) Fundamental examples of ∞-categories such as the ∞-category of spectra (4) Additional topics depending on participants’ background Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (09.09.2025)
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Familiarity with the following concepts will be assumed. (1) Basic category theory ((co)limits, functors, Yoneda embedding) (2) Basic point set topology (topological spaces, continuous maps, homotopy) (3) algebraic topology (fundamental group, homotopy groups and singular homology of a topological space, CW complexes) The course may be followed without prior knowledge of algebraic topology but many concepts and ideas for ∞-categories are directly related to or inspired by these notions. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (09.09.2025)
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