Final Answers
© 2000-2022 Gérard P. Michon, Ph.D.

Topoi

On the delusion of absolute rigor:

Chaque époque vit dans l'illusion qu'elle crée
la rigueur absolue. Chaque époque se trompe.
Pierre Cartier (2014)

Presheaves and sheaves.
Bohr topos.
Elementary topos (Lawvere).
Grothendieck topos.
Kochen-Specker theorem. Categorial expression of quantum theory.

Related Links (Outside this Site)

What is a Topos? (AMS, Oct. 2004) by Luc Illusie (1940-, Ph.D. 1971).
Topos Theory in a Nutshell (2005-04-12) by John C. Baez (1960-).
An informal introduction to topos theory (2010, 2011) by Tom Leinster.

Blogs & Forums : Topos in nLab.
Sean Moss reviews (2014) "On a Topological Topos" by Peter Johnstone.

Wikipedia : History of topos theory | Topos

Bibliography :
"Topos Theory" (1977) by Peter T. Johnstone (1948-).
"Toposes, Triples and Theories" (1985, 2005) Michael Barr, Charles Wells.
"Topoi: The Categorial Analysis of Logic" (2006) by Robert Goldblatt.

Videos : A topos for algebraic quantum theory by Chris Heunen (January 2008, Imperial College London).
Olivia Caramello interviewed by Stéphane Dugowson & Anatole Khelif (2014).
Olivia Caramello (3:06) (Laurence Honorat, 2014-10-16).

Topos: Opening Lecture (1:06:35) by Pierre Cartier (IHES, 2015-11-23).
Crash course in topos theory [ 1 | 2 | 3 | 4 ] by André Joyal (IHES, 2015).
Categorial logic, classifying toposes & bridge technique, by Olivia Caramello
(IHES, 2015-11-23) [ 1:19:28 | 1:19:59 | 1:16:24 | 1:17:49 ]
Panel (1:04:30) Olivia Caramello, André Joyal, Laurent Lafforgue, Alain Connes.

Toposes: Nice Places to Do Math (2:01) MathProofsable (2017-01-09).
Topos and Information (1:18:05) by Daniel Bennequin (IHES, 2018-04-12).
Grothendieck's 1973 topos lectures (1:31:08) by Colin McLarty (2018-05-03).
Glances at topos theory [ 1 | 2 | 3 | 4 | 5 | 6 ] by Francis Borceux (2018-09-20).

La notion unificatrice de topos (2:06:28) by Olivia Caramello (2018-03-06).
Un topo sur les topos (1:57:30) by Alain Connes (in French, 2018-10-07).
Topos de Grothendieck (37:09) by Stéphane Dugowson (December 2014).

Synthetic prequantum field theory (1:16:12) by Urs Schreiber (2015-12-03).

Topos

The ideas of topos was born on Monday, April 21, 1958
[from a remark made by Grothendieck after a lecture of Serre]
Colin McLarty (1951-)

(2019-01-15) Presheaf & Sheaf (French: préfaisceau & faisceau). If something occurs, it occurs on a neighborhood of every point.

A sheaf on a topological space Come back later, we're
still working on this one...

Sheaf | Stalk

Introduction to Sheaf Theory (57:39) by Geoff Vooys (2018-10-12).

(2014-12-25) Bohr Topos Underlies Jordan algebras.

In 1932, Pascual Jordan tried to isolate some axioms that an "algebra of observables" should satisfy when associativity is not assumed (cf. nLab).