Reading Seminar: Topos Theory (Fall 2021)

Essential information

  • Organized by: Dan Christensen and Chris Kapulkin.
  • Time: Tuesdays at 1:30 PM in Winter 2022; Mondays at 1:30 in Fall 2021.
  • Location: MC 107.
  • In January and February 2022, the seminar will be on hiatus due to the Omicron variant. (We won't be going online.)

Textbook

We will follow:

  • S. Mac Lane, I. Moerdijk, Sheaves in Geometry and Logic, 1992. Referred below as [MM]

We will assume familiarity with the chapter "Categorical Preliminaries" of that book.

Other excellent sources include:

  • P.T.J. Johnstone, Topos Theory, 1977.
  • P.T.J. Johnstone, Sketches of an Elephant: A Topos Theory Compendium, Vols. 1-2, 2002.
  • J. Lambek, P. Scott, Introduction to higher order categorical logic (Part 2), 1986

Schedule

Fall 2021

  • Sept 20: Introduction and Organization. Unidentified organizer.
  • Sept 27: Subobject classifiers [MM I.2-4]. By Jarl G. Taxeras Flatten.
  • Oct 4: Exponentials [MM I.6]. By Udit Mavinkurve.
  • Oct 11: Thanksgiving Day, no seminar.
  • Oct 18: Categories and logic [MM I.7-9]. By Dimitrios Thanos.
  • Oct 25: Introduction to sheaves [MM II.1-3]. By Jacob Fabe.
  • Nov 1: Fall Reading Week, no seminar.
  • Nov 8: Sheaves as étale spaces [MM II.6 and II.9]. By Mohabat Tarkeshian.
  • Nov 15: Grothendieck topologies [MM III.2]. By Brittania Fusca.
  • Nov 22: Categories of sheaves on a site [MM III.4-5]. By Jinho Kim.
  • Nov 29: Grothendieck toposes [MM III.6-7]. By Artem Gureev.
  • Dec 6: Exponentials in an elementary topos [MM IV.1-2]. By Karthik Boyareddygari.

Winter 2022

  • Mar 1: Colimits, part 1 [MM IV.3-5]. By Artem Gureev.
  • Mar 8: Colimits, part 2 [MM IV.3-5]. By Jarl G. Taxeras Flatten.
  • Mar 15: Factorization [MM IV.6]. By Jinho Kim.
  • Mar 22: Slice of a topos is a topos [MM IV.7]. By Karthik Boyareddygari.
  • Mar 29: Internal Heyting algebras [MM IV.8]. By Mohabat Tarkeshian.
  • Apr 5: The Beck-Chevalley condition [MM IV.9]. By Udit Mavinkurve.
  • End of term.

 


 For more information, please contact Chris Kapulkin.