NOTE: Lectures will start on March 31 and will be held Tuesdays and
Thursdays 10-11:30 in 2005VH. I have prepared lecture notes covering the
first third of the course. Please email me to request a copy.
Sheaf theory is one of the key elements in Grothendieck's rewriting
modern algebraic geometry. It led him to the notion of topos which was
generalized by Lawvere and Tierney who established an astonishing link
between geometry and logic. The course provides some basic elements of
and sheaf theory. Beyond the applications to geometry and logic we will
discuss the role of topos theory in quantum physics and computing.
Although basic categorical notions and tools will be reviewed as needed,
students without prior knowledge of basic elements of category theory
advised to undertake some reading prior to the course. MATH 6120 is a
Evaluation will be based at 50% on 5 home work assignments; 20 % on a
special individual project, 30 % on a final test.
Here are some useful books on the subject of the course (ordered
F. Borceux: Handbook of Categorical Algebra, vol. 3. Cambridge
University Press 1994.
R. Goldblatt: Topoi - The Categorical Analysis of Logic. Elsevier 1984.
Reprint: Dover 2006.
P. T. Johnstone: Topos Theory. Academic Press, London 1977.
S. MacLane and I. Moerdijk: Sheaves in Geometry and Logic, A First
to Topos Theory. Springer 1992.
C. McLarty: Elementary Categories, Elementary Toposes. Oxford University
M.-C. Pedicchio, W. Tholen (editors): Catgorical Foundations. Cambridge
University Press 2004. (Chapter VII only, by C. Centazzo and E. Vitale.)