Learning Topos Theory

I want to learn Topos Theory as a first venture into categorical/categorial logic. My current understanding of the motivation for topos theory is that its a means of generalising/swapping out the models of a mathematical theory, which is usually occupied by set theory. I’m particularly intrigued about the connection between geometry and logic.

Resources

I should warn that these descriptions are written before fully reading the content, so they may be naive.

Textbooks

• Robert Goldblatt - The Categorial Analysis of Logic
• MacLane and Moerdijk - Sheaves in Geometry and Logic
• Bartoz Milewski - Category Theory For Programmers

Videos

• Daniel Murfet - Topos Theory Seminar
  • Notes
• Bartoz Milewski - Category Theory For Programmers (Preface)
  • Video Lectures Part I, II, III
  • Textbook
  • General background on Category Theory, which builds towards some applications including monads, topoi and Lawvere Theories (see part III).
• Brendan Fong, Bartosz Milewski, and David Spivak - MIT 18.S097 - Programming with Categories
  • Lecture Notes
  • Lecture Videos
  • Discussion Forum
• MathProofsable - Category Theory: Toposes
• MathProofsable - Category Theory: First Order Logic
• Steve Awodey - Natural Models of Type Theory

Posts/Notes

• John Baez - Topos Theory in a Nutshell
• John Baez - Categories, Quantization and much more
• Daniel Murfet - Foundations for Category Theory
• Tom Leinster - An informal introduction to topos theory
• Ieke Moerdijk & Jaap Van Oosten - Basic Category Theory and Topos Theory: Lecture Notes
  • From the mastermath course Category Theory and Topos Theory
• Ieke Moerdijk & Jaap Van Oosten - Topos Theory: Preliminary Lecture Notes
• Peter Johnstone - Sketches of An Elephant: A Topos Theory Compendium
  • Book Review by Steve Awodey

Non-introductory topics

• Peter Johnstone - Topos-theoretic models of the continuum