Topos theory is the part of category theory that studies categories which are toposes. This includes in particular Grothendieck toposes, i.e. categories of sheaves.
There are always two ways to think of topos theory: as being
A gentle basic introduction is
A quick introduction of the basic facts of Grothendieck topos theory is chapter I, “Background in topos theory” in
Other introductions include
Tom Leinster, An informal introduction to topos theory (2010)
André Joyal, A crash course in topos theory – The big picture, lecture series at Topos à l’IHES, November 2015, Paris
André Joyal, Geometric aspects of topos theory in relation with logical doctrines, talk at New Spaces for Mathematics and Physics, IHP Paris 2015 (video recording)
The mother of it all though not exactly a textbook
A still very useful reference is the monograph
This later grew into the more detailed
Maybe the standard modern textbook on Grothendieck toposes is
A thorough but clear first introduction to topos theory is
Introducing even category theory from the scratch while still managing to cover some ground, the following textbook is the royal road to topos theory for people with some background in first-order logic:
Similarly, the following monograph develops topos theory to considerable depth without categorical prerequisites
See also
A survey is in
A nice and concise introduction is available in
Francis Borceux, Some glances at topos theory , lecture notes Como 2018. (pdf)
Ieke Moerdijk, Jaap van Oosten, Topos theory Master Class notes (2007) (pdf)
F. William Lawvere, Comments on the development of topos theory, pp.715-734 in Pier (ed.), Development of Mathematics 1950 - 2000 , Birkhäuser Basel 2000. (tac reprint)
Colin McLarty, The Uses and Abuses of the History of Topos Theory , Brit. J. Phil. Sci., 41 (1990) (JSTOR) PDF
A historical analysis of Grothendieck’s 1973 Buffalo lecture series on toposes and their precedents is in
Colin McLarty, Grothendieck’s 1973 topos lectures, Séminaire Lectures grothendieckiennes, 3 May (2018) (YouTube video)
Last revised on July 27, 2018 at 05:07:00. See the history of this page for a list of all contributions to it.