T
Introduction vjj
Chapter I - Sup-lattices , , 1
1. Definitions andduality 1
2. Limits and colimits 2
3. Free sup-lattices 3
4. Sub andquotient lattices 4
5. Tensor products 5
Chapter II - Rings, modules and descent 7
1. Rings andmodules 7
2. Tensor product of modules 8
3. Change of rings 9
4. Flatness, projectivity, andpurity 11
5. . Descent theory formodules . . 12
Chapter III - Locales 21
1. Locales andcommutative monoids 21
2. Limits and colimits . 21
3. Thefree locale 22
4. Local operators andquotients 22
5. The splitting locale 25
Chapter IV - Spaces 27
1. Subspaces 27
2. Points and discrete spaces 28
3. The Sierpinski space 29
4. Pullbacks and projective limits 30
5. The splitting space 31
Chapter V - Open maps of spaces 3 3
1. Open maps - definition 33
2. Open subspaces 34
3. Conditions for openness 35
4. Open surjections, pullbacks 38
5. A characterization of discrete spaces 40
Chapter VI - Change of base 42
1. Change of base for sup-lattices and locales 42
A°P
A°P
2. Determination of si(S- ) and loc(S- ) 46
3. Determination of s£(sh(A)) and loc(sh(A)) for A e loc(S) . . . 49
4. The Beck-Che valleyv conditions 52
5. The spatial reflection 53
Chapter VII - Open morphisms of topoi 56
1. Open geometric morphisms 56
2. A site characterization of openness 58
3. The spatial cover 59
4. A characterization of atomic topoi 61
Chapter VIII - Descent morphisms of topoi 64
1. Effective descent morpnisms 64
2. Open surjections 65
3. Applications to the structure of topoi 68
References 71
v
Previous Page Next Page