Institut für Mathematik Universität Zürich | Deutsch English Français Italiano | |

Categories, Sheaves, and Locales

Seminar by Christian Dahlhausen in autumn term 2018/19.

Tuesday 15-17, Y27 H25

Contents

This seminar provides an introduction to the basic notions of category theory and sheaf theory which both are ubiquitous in pure mathematics and very useful in many contexts. As an application, we will deal in the end with the question whether one could reconstruct a topolological space from only knowing its poset of open subsets. The theory of locales will help us to answer this question.Literature

- Bredon, Glen E.:
*Sheaf Theory*. Graduate Texts in Mathematics 170 (2nd ed.), Springer, 1997. - Johnstone, Peter T.:
*Stone spaces*. Cambridge Studies in Advanced Mathematics, vol. 3, Cambridge University Press, 1982. - Kashiwara, Masaki and Schapira Pierre:
*Sheaves on manifolds*. Grundlehren der mathematischen Wissenschaften, vol. 292, Springer, 1994. - Kashiwara, Masaki and Schapira Pierre:
*Categories and Sheaves*. Grundlehren der mathematischen Wissenschaften, vol. 332, Springer, 2006. - Mac Lane, Saunders and Moerdijk, Ieke:
*Sheaves in Geometry and Logic. A first introduction to topos theory*. Corrected reprint of the 1992 edition. Universitext, Springer, 1994. - Riehl, Emily:
*Category theory in context*. Aurora: Dover Modern Math Originals, 2016. (available online)

Talks

No. | Date | Title |

0 | 17.09. | Overview and organisatorial stuff |

1 | 01.10. | Set theory, universes, and categories |

2 | 08.10. | Functors and natural transformations |

3 | 15.10. | Limits and colimits |

4 | 22.10. | Adjoint functors |

5 | 29.10. | Presheaves and sheaves |

6 | 05.11. | Stalks and sheafification |

7 | 12.11. | Sheaves as étalé spaces |

8 | 19.11. | Frames and locales |

9 | 26.11. | Points and sober spaces |

10 | 03.12. | Spatial locales and sober spaces |