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Introduction to Infinity-Categories
Provider: Faculty of Science

Activity no.: 5575-17-07-31 
Enrollment deadline: 28/04/2017
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time25.04.2017, at: 13:00 - 22.06.2017, at: 15:00
Regular seats30
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserRune Gjøringbø Haugseng    E-mail address: haugseng@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 4
Block noteTuesdays and Thursdays from 13:00 to 15:00 - at the 4th floor seminar room (04.4.01).
Exam formContinuous assessment
Exam formOne internal examiner
Exam detailsParticipants will each give one 2x45-minute lecture during the course.

Aim and content
After completing the course, the students will have:

* Knowledge of the material mentioned in the description of the content.
* Skills to read and understand research papers concerning topics discussed in lectures.

The following competences:

* Have a good overview and understanding of the theory of quasicategories and how they give a useful language for homotopy theory.
* Master (at a satisfactory level) the fundamental results covered in the lectures, to the extent of understanding their proofs and being able to interconnect various results.

The first part of the course will develop the basics of the theory of quasicategories (equivalences, joins and slices, limits and colimits, the Joyal model structure, fibrations). The second part will cover a selection of more advanced topics in less detail - the exact topics will depend on the interests of the participants, but may include: stable infinity-categories, (co)Cartesian fibrations and straightening, presentable infinity-categories and the adjoint functor theorem, monads and the Barr-Beck-Lurie theorem, symmetric monoidal infinity-categories, infinity-operads, Segal spaces, infinity-topoi.

Some familiarity with simplicial sets and model categories is required.

Literature
The course will not follow a particular book. Relevant references include:

Cisinski, Higher category theory and homotopical algebra
Groth, A short course on infinity-categories
Rezk, Lecture notes on quasicategories
Lurie, Higher topos theory

Teaching and learning methods
Two 2x45-minute lectures per week.

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