n
Categories,
functors, natural transformations
n
Adjoint
functors, examples from set theory, algebra and topology
n
Limits
and colimits, completeness and cocompleteness
n
Yoneda
Lemma, Yoneda embedding, Kan extensions
n
Cartesian
closedness, toposes
n
Factorization
systems, fibrations, topological functors
Individual Project Topics
n
Monads,
monadicity criteria
n
Monoidal
categories, enriched category theory
n
Abelian
and semiabelian categories
n
Monadquantaleenriched
categories
There
is no single recommended text for the course, but see below for
a list of recommended books.
Evaluation
will be based on

5 homework assignments, to be counted at 10% each toward your
final grade,

an individual project to be counted at 20%,

a final test, counting 30%.
Recommended Books:
Tom
Leinster, Basic Category Theory, Cambridge University Press
2014, available on line at https://arxiv.org/abs/1612.09375
Steve
Awodey, Category Theory, Oxford University Press 2006.
Francis
Borceux, Handbook of Categorical Algebra 13, Cambridge
University Press 1994.
Saunders
Mac Lane, Categories For the Working Mathematician (2nd
Edition), Springer 1997.
F.
William Lawvere and Stephen H. Schanuel, Conceptual Mathematics,
A first introduction to categories, Cambridge University Press
1997.
Jiri
Adamek, Horst Herrlich and George E. Strecker, Abstract and
Concrete Categories, The Joy of Cats, Wiley 1990; available
online at http://tac.mta.ca/tac/reprints/articles/17/tr17abs.html
.
Michael
Barr and Charles Wells, Toposes, Triples and Theories, Springer
1985; available on line at http://tac.mta.ca/tac/reprints/articles/12/tr12abs.html
.
Dirk
Hofmann, Gavin J. Seal, Walter Tholen (editors), Monoidal
Topology, A Categorical Approach to Order, Metric and Topology,
Cambridge University Press 2014. Preliminary
version