Introduction | p. 1 |
Distributions and Complete Spreads | |
Lawvere Distributions on Toposes | p. 9 |
Basic Background in Topos Theory | p. 9 |
Essential and Locally Connected Geometric Morphisms | p. 12 |
Topos Frames and Distributions | p. 14 |
Cosheaves and the Bergman Functor | p. 19 |
Definable Dominances | p. 26 |
Complete Spread Maps of Toposes | p. 31 |
Fox Complete Spreads | p. 32 |
Pure Geometric Morphisms | p. 36 |
Model Amalgamation | p. 43 |
Discrete Opfibrations and Complete Spreads | p. 46 |
Properties of Complete Spreads | p. 51 |
The Spread and Completeness Conditions | p. 55 |
Spreads | p. 55 |
Zero-dimensionality | p. 63 |
Components-generated Spreads | p. 65 |
Amalgamation and Fibrations | p. 69 |
The Completeness Condition | p. 72 |
An Axiomatic Theory of Complete Spreads | |
Completion KZ-Monads | p. 79 |
KZ-Adjointness | p. 79 |
The Symmetric Monad | p. 82 |
Algebras and Cocompleteness | p. 87 |
| |
Complete Spreads as Discrete M-fibrations | p. 99 |
Discrete (op)fibrations Relative to M | p. 99 |
Complete Spreads as Discrete Fibrations | p. 101 |
A Pullback-preservation Theorem for Presheaves | p. 103 |
Closed and Linear KZ-Monads | p. 109 |
Closed KZ-Monads and Comprehension | p. 109 |
The Gleason Core and Density Axioms | p. 114 |
The Twisted Single Universe | p. 118 |
Linear KZ-Monads | p. 120 |
Pitts' Theorem Revisited | p. 124 |
Aspects of Distributions and Complete Spreads | |
Lattice-Theoretic Aspects | p. 131 |
Monadicity Theorem | p. 131 |
The Structure of Distribution Algebras | p. 135 |
Relative Stone Locales | p. 141 |
On a version of the Heine-Borel Theorem | p. 150 |
The Entire Completion of a Spread via Forcing | p. 152 |
Localic and Algebraic Aspects | p. 161 |
Distributions on Locales | p. 161 |
Symmetric versus Lower Bagdomain | p. 167 |
Discrete Complete Spread Structure | p. 172 |
Algebraic Geometry: Coschemes | p. 175 |
Distributions on the Jonsson-Tarski Topos | p. 183 |
Topological Aspects | p. 189 |
Locally Constant versus Unramified Coverings | p. 190 |
Purely Skeletal Geometric Morphisms | p. 198 |
Branched Covering Toposes | p. 202 |
The Index of a Complete Spread | p. 209 |
Bibliography | p. 217 |
Index | p. 223 |
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