Sketches of an Elephant: A Topos Theory Compendium: Volume 2Clarendon Press, 12 Eyl 2002 - 716 sayfa Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and thereby to demonstrate the overall unity of the subject. The material is organized in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text. |
İçindekiler
B1 Indexed categories and fibrations 235 | 464 |
Bibliography follows p | 467 |
F3 The free topos | 468 |
C1 Sheaves on a locale | 471 |
C2 Sheaves on a site | 536 |
C3 Classes of geometric morphisms | 606 |
C4 Local compactness and exponentiability | 711 |
C5 Toposes as groupoids | 755 |
F3 The free topos | 970 |
Predicative type theories | 976 |
Axioms of choice and booleanness | 987 |
De Morgans law and the Gleason cover | 998 |
Real numbers in a topos | 1012 |
D5 Aspects of finiteness | 1033 |
Finite cardinals | 1041 |
Finitary algebraic theories | 1049 |
TOPOSES AS THEORIES | 805 |
D1 Firstorder categorical logic | 807 |
Categorical semantics | 817 |
Firstorder logic | 828 |
Syntactic categories | 841 |
Classical completeness | 852 |
D2 Sketches | 861 |
Sketches and theories | 868 |
Sketchable and accessible categories | 874 |
Properties of model categories | 882 |
D3 Classifying toposes | 890 |
The object classifier | 901 |
Coherent toposes | 910 |
Boolean classifying toposes | 918 |
Conceptual completeness | 931 |
D4 Higherorder logic | 940 |
ACalculus and cartesian closed categories | 951 |
Toposes as type theories | 963 |
Kuratowskifiniteness | 1058 |
Orbitals and numerals | 1075 |
Bibliography follows p | 1089 |
CONTENTS VOLUME | 1 |
Whilst I am on that subject I should also record my indebtedness to another of my former | 3 |
F4 Topos theory and set theory | 6 |
Cartesian categories | 11 |
E2 Algebraic homotopy theory | 12 |
| 18 | |
| 20 | |
| 30 | |
| 33 | |
A2 Toposes basic theory 68 | 38 |
A3 Allegories 130 | 47 |
| 55 | |
| 56 | |
| 61 | |
Diğer baskılar - Tümünü görüntüle
Sık kullanılan terimler ve kelime öbekleri
A₁ arbitrary atomic axiom Beck-Chevalley condition BTop/S canonical cartesian closed CjSLat codomain coequalizer coherent commutative compact composite construction Cont(G coproduct corresponding covering deduce defined definition denote dense diagram element epimorphism equivalent fact factors fibration fibrewise filtered colimits follows forgetful functor frame homomorphism full subcategory functor F geometric morphism given Grothendieck topos hence Heyting hyperconnected inclusion Ind-C induced injective internal locale inverse image functor isomorphism J-covering K-finite lattice left adjoint Lemma local homeomorphism locally connected logic Math monic monoid monomorphism Morgan's law morphism f natural number object natural transformation obtain open sublocales poset preserves finite Proof Proposition provable pullback regular resp retract right adjoint S-indexed S-topos satisfies semilattice sequent Sh(C Sh(X Sh(Y sheaf sheaves sieve simply space subobject subsets subterminal objects suppose surjective T-model terminal object theorem theory topology toposes unique verify