Topos theory
Overview
Generalized spaces that behave like categories of sheaves. Grothendieck toposes arise in algebraic geometry; elementary toposes (Lawvere–Tierney) provide a categorical foundation for logic.
Era: 1960s–1970s
Proposed at: Bures-sur-Yvette, France (IHES)
Formal structure
Domain: Topos E: category with finite limits, exponentials, subobject classifier Ω
Ω = {0,1} in Set; Ω^X = subobjects of X; ⊢: 1 → Ω
Constraints: Lawvere–Tierney topology j: Ω → Ω; sheaves = j-closed objects
Objective: Internal logic; geometric morphisms; classifying toposes