Categorical Geometry Home Page

Categorical Geometry

Zhaohua Luo

          Introduction
          Chapter 1. Analytic Categories
            1.1 Strong Monos
            1.2 Analytic Categories
            1.3 Distributive Properties
            1.4 Coflat Maps
            1.5 Beck-Chevalley Conditions
            1.6 Analytic Monos
            1.7 Disjunctable Objects
          Chapter 2. Analytic Topologies
            2.1 Normal Sieves
            2.2 Normal Monos
            2.3 Divisors
            2.4 Analytic Sieves
            2.5 Framed Topologies
            2.6 Analytic Topologies
        Chapter 3. Analytic Geometries
            3.1 Reduced Objects
            3.2 Integral Objects
            3.3 Simple Objects
            3.4 Local Objects
            3.5 Analytic Geometry
            3.6 Spectrums
            3.7 Coflat Disjunctable Analytic Categories
            3.8 Regular Objects
        Chapter 4. Coherent Analytic Categories (Preliminary)
            4.1 Locally Finitely Copresentable Categories
            4.2 Coherent Analytic Categories
            4.3 Extensive Topologies
            4.4 Stone Geometries
        Chapter 5. Coherent Analytic Geometries (Preliminary)
            5.1 Coherent Analytic Geometries
            5.2 Localizations
            5.3 Local Isomorphisms
            5.4 Strict Coherent Analytic Geometries
            5.5 Local Properties of maps
            5.6 Open Coflat Maps (new, 11/15/98)
            5.7 Faithfully Coflat Maps (new, 11/15/98)