In February 2024 prof. Matías Menni will teach a course at the PhD in Mathematics at Unisa. The title is Presheaves in Geometry and Logic, a preface to Topos Theory, a short description follows. The course will take place on Mondays at Wednesdays from 14:00 to 16:00 in room P19.
Description
Presheaves in Geometry and Logic, a preface to Topos Theory.
We will use categories of presheaves in order to illustrate Exactness (in non-linear contexts), Extensivity, Cartesian Closure, existence of Subobject Classifiers, and their use in simple geometric constructions such as spaces of connected components or collapses of subspaces. Familiarity with presheaf toposes, their properties and their manipulation will motivate the definition of elementary toposes and give the student indispensable tools to become acquainted with Grothendieck toposes.
Bibliography
- Johnstone, P. T. J. Sketches of an elephant. Oxford: Clarendon Press 2002.
- La Palme Reyes, M., Reyes, G. E. and Zolfaghari, H. Generic figures and their glueings. Polimetrica 2004.
- Lawvere, F. W. and Schanuel, S. H. Conceptual Mathematics (2nd ed.). CUP 2009.
- Lawvere, F. W. and Rosebrugh, R. Sets for Mathematics. CUP 1997.
- Mac Lane, S. and Moerdijk, I. Sheaves in Geometry and Logic. Universitext 1992.
