module Elephant where

Sketching the elephant🔗

Though the 1Lab is not purely a formalization of category theory, it does aim to be a useful reference on the subject. However, the 1Lab organizes content in a highly non-linear fashion; this can make it somewhat difficult to use as a companion to more traditional resources.

This page attempts to (somewhat) rectify this situation by gathering all of the results from “Sketches of an Elephant – A Topos Theory Compendium” (Johnstone 2002) in a single place.1

A. Toposes as categories🔗

A1 Regular and cartesian closed categories🔗

A1.1 Preliminary assumptions🔗

A1.2 Cartesian Categories🔗

A1.3 Regular Categories🔗

A1.4 Coherent Categories🔗

A1.5 Cartesian closed categories🔗

A1.6 Subobject classifiers🔗

C Toposes as spaces🔗

C2 Sheaves on a site🔗

C2.1 Sites and coverages🔗

C2.2 The topos of sheaves🔗

See topos of sheaves.

  1. It also serves as an excellent place to find possible contributions!↩︎


  • Johnstone, Peter T. 2002. Sketches of an Elephant: a Topos Theory Compendium. Oxford Logic Guides. New York, NY: Oxford Univ. Press.