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Syllabus Category Theory - 80779
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Last update 21-08-2018
HU Credits: 2

Degree/Cycle: 2nd degree (Master)

Responsible Department: Mathematics

Semester: 1st Semester

Teaching Languages: Hebrew

Campus: E. Safra

Course/Module Coordinator: Mr. Lior Yanovski

Coordinator Email:

Coordinator Office Hours: By appointment

Teaching Staff:
Prof Tomer Schlank

Course/Module description:
Introductory course in category theory for 3rd year undergraduate students and 1st year graduate students.

Course/Module aims:
Familiarity with the basic concepts and theorems of category theory and proficiency in the categorical language with emphasis on examples.

Learning outcomes - On successful completion of this module, students should be able to:
See course aims.

Attendance requirements(%):

Teaching arrangement and method of instruction: Lecture

Course/Module Content:
The course will cover the following topics:

1. Categories, functors & natural transformations: definitions, examples, basic constructions.

2. Universal properties, representable functors, Yoneda lemma.

3. (co)limits: definitions & examples, special kinds (finite, connected, filtered etc.)

4. (co)limit calculus:
commutation, functors preserving (co)limits, cofinality etc.

5. Adjoint functors: definitions, examples and basic properties. The adjoint functor theorem (?).

In addition, it will cover some of the following topics:

6. More on (co)limits: Kan extensions, (co)ends, weighted (co)limits.

7. Sheaves, localization and topoi: definitions, examples, characterization.

8. Abelian categories: definitions & examples, intro to homolgical algebra, the embedding theorem.

9. Monoidal categories.

10. Intro to 2-categories.

Required Reading:

Additional Reading Material:

Course/Module evaluation:
End of year written/oral examination 100 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %

Additional information:
This is an introductory course in category theory with emphasis on the categorical language and examples.
Students needing academic accommodations based on a disability should contact the Center for Diagnosis and Support of Students with Learning Disabilities, or the Office for Students with Disabilities, as early as possible, to discuss and coordinate accommodations, based on relevant documentation.
For further information, please visit the site of the Dean of Students Office.