Category Theory WM033C, lectures, Fall 2013
General information on this course can be found in the
studiegids. Please don't forget to register in
blackboard for this course, in order to receive (email) announcements.
Lectures for this course will be on Tuesday mornings, 10:45-12:30, at
different locations
(check studiegids). The exercise course is on Thursday
mornings, 8:45-10:30, also at different locations.
Information about the exercises can be found here.
Course material
The book that will be used
is: Steve Awodey, Category Theory. Separate chapters of
the book are available via the
authors webpage.
From this book the following material will be skipped. The
numbers refer to the chapters
available online.
- Chapter 1: 1.5: the two theorems; 1.7: the free category
construction; 1.8 entirely.
- Chapter 2: 2.3 entirely; 2.6.(6) type theory
- Chapter 3: from Example 3.22 onwards
- Chapter 4: entirely skipped
- Chapter 5: from example 5.29 onwards
- Chapter 6: sections 6.4 and 6.6.
- Chapter 7: 7.2 and 7.3 and 7.7 from 7.20 onwards, 7.8.
- Chapter 8: 8.6 and lemma 8.12 and the proof of 8.13, all of 8.8.
- Chapter 9: section 9.5; propositions 9.16, 9.17;
section 9.7 from example 9.22 onwards; section 9.8.
Lectures summary
- Lecture 1, 3/9: general introduction, covering roughly
pages 1-7
of chapter
1.
- Lecture 2, 5/9: the definition of functor, and many examples;
isomorphisms, product and opposite category.
- Lecture 3, 10/9: further constructions on categories
(slice, arrow), free monoid on a set, monos and epis.
- Lecture 4, 17/9 (by Bas Westerbaan): sections,
retractions, (co)products and initial/final objects.
- Lecture 5, 24/9 (by Robert Furber): products and limits
- Lecture 6, 1/10: coproducts
- Lecture 7, 8/10: coequalisers and pullbacks
- Lecture 8, 15/10: limits (once again), and exponentials
- Lecture 9, 22/10: more about exponentials, especially in
the poset case (Heyting algebras) and natural transformations
- Lecture 10, 12/11: functor categories, and equivalence of
categories.
- Lecture 11, 26/11: Yoneda Lemma, and its consequences
- Lecture 12, 3/12: Adjunctions: definitions and simple examples
- Lecture 13, 10/12: Adjunctions: properties and more
(non-trivial) examples