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Johnstone P.T. — Sketches of an Elephant: A Topos Theory Compendium
Johnstone P.T. — Sketches of an Elephant: A Topos Theory Compendium

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Название: Sketches of an Elephant: A Topos Theory Compendium

Автор: Johnstone P.T.


Citing the old Indian story about the blind men feeling different parts of an elephant and coming up with divergent descriptions of the animal Johnstone (mathematics, U. of Cambridge, UK) says that topos theory can be described in divergent ways depending on what part is examined. The original conception of toposes arose in the 1960s as a "generalized space" supporting cohomology theory, but has grown to be used by category theory and other branches of mathematics. Addressing those already familiar with topos theory, Johnstone offers these volumes (and a scheduled 3rd) as a complete treatment of all of the pieces of elementary topos theory together with fully worked-out results. Volume one discusses toposes as categories. Toposes as spaces and theories are reserved for the second. The final volume expected to discuss homotopy and cohomology, and toposes as mathematical universes.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 1089

Добавлена в каталог: 31.03.2008

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Предметный указатель
$\infty$-pretopos      A1.4.19
$\infty$-pretopos, $\mathcal{S}$-indexed      B3.3.9
$\lambda$-calculus      D4.2.1
$\lambda$-calculus, extended      D4.2.16
$\lambda$-calculus, typed      D4.2.1
$\lambda$-calculus, untyped      D4.2.16
$\mathcal{V}$-category      B2.1.1
$\mathcal{V}$-embedding      B2.1.1
$\mathcal{V}$-enrichment      B2.1.2
$\mathcal{V}$-functor      B2.1.1
$\mathcal{V}$-natural transformation      B2.1.1
$\mu\lambda$-calculus      D4.4.1
$\mu\lambda$-calculus, cartesian      D4.4.5
$\mu\lambda$-calculus, full      D4.4.5
$\sigma$-pretopos      A1.4.19
$\Sigma$-structure      D1.2.1 D4.1.4
$\Sigma$-structure, homomorphism of      D1.2.1
$\tau L$-calculus      D4.3.16
$\tau$-calculus      D4.3.1
2-category      B1.1.1
2-category, locally ordered      A3.1.2
2-cell      B1.1.1
2-functor      B1.1.2
Adjoint (in a 2-category)      B1.1.2
Adjoint (in a 2-category), weak      B1.1.8
Adjoint retract      B1.1.9
Algebra (for algebraic theory)      D1.2.15(a)
Algebra (for algebraic theory), free      D5.3.5
Algebra (for an endofunctor)      A1.1.4
Allegory      A3.2.1
Allegory, distributive      A3.2.13
Allegory, division      A3.4.1
Allegory, effective      A3.3.9
Allegory, geometric      A3.2.12
Allegory, positive geometric      A3.2.12
Allegory, positive union      A3.2.11
Allegory, power      A3.4.5
Allegory, pre-tabular      A3.3.6
Allegory, syntactic      D1.4.15 D4.3.9
Allegory, tabular      A3.2.3
Allegory, union      A3.2.11
Apartness relation      D4.7.6
Arithmetic operations      A2.5.4
Arithmetic operations on numerals      D5.5.14
Arithmetic operations on R      D4.7.8
Arity      D1.1.1
Associated sheaf functor      A4.1.8 A4.4.4 C2.2.6
Associated split fibration      B1.3.10
atom      C3.5.7
Atomic proposition      D1.1.1
Atomic system      D3.4.13
Atomic topos      C3.5.1
Axiom of Choice      D4.5.1(b) D4.5.4
Axiom of theory      D1.1.6
Axiom, distributive      D1.3.1(i)
Axiom, Frobenius      D1.3.1(i)
Axiom, geometric      B4.2.7(b)
Axiom, identity      D1.3.1(a)
Axiom, logical      D1.3.1
Axiom, non-logical      D1.1.6
Bag of T-models      B4.4.15
Bagdomain, lower      B4.4.17
Bagdomain, upper      B4.4.21(c)
Basis (for locale)      C2.2.4(b)
Beck-Chevalley condition      A1.4.11 A2.2.4 A4.1.16 B1.4.2
Beck-Chevalley condition, weak      A4.1.16
Beck-Chevalley morphism      C2.4.16
Beck-Chevalley morphism, stable      C2.4.16
Beck-Chevalley morphism, weak      C2.4.16
Beth Definability Theorem      D3.5.2
Bicategory      B1.1.2
Bimodule (between internal categories)      B2.7.1
Biseparated functor      C2.2.13
Bisite      C2.2.13
Bound (for topos over $\mathcal{S}$)      B3.1.7
Bound (for topos over $\mathcal{S}$), pre-      D3.2.3
C-monoid      D4.2.15
Cantor diagonal argument      D4.1.8
Cantor-Bernstein theorem      D4.1.11
capitalization      D1.5.3
Cardinal, finite      A2.5.14 D5.2.1
Cardinal, generic finite      A2.5.14
Cardinal, limit power      A2.1.2
Cartesian closed category      A1.5.1
Cartesian closed category, locally      A1.5.3
Cartesian closed category, properly      A1.5.1
Category, $\kappa$-accessible      D2.3.1
Category, $\kappa$-filtered      D2.3.1
Category, $\kappa$-Heyting      D3.1.19
Category, $\mathcal{V}$-enriched      B2.1.1
Category, $\sigma$-coherent      A1.4.19
Category, *-autonomous      C1.1.7
Category, accessible      D2.3.1
Category, balanced      A1.1.1
Category, Barr-exact      A1.3.6
Category, Boolean coherent      A1.4.10
Category, cartesian      A1.2.1
Category, cartesian closed      A1.5.1
Category, Cauchy-complete      A1.1.10
Category, co-slice      A1.1.6
Category, coherent      A1.4.1
Category, concrete      A1.1.5
Category, continuous      C4.2.7
Category, cowell-powered      A1.4.17
Category, disjunctive      B1.5.10 D1.3.6
Category, effective regular      A1.3.6
Category, enriched      B2.1.1
Category, essentially small      B2.3.4
Category, exact      A1.3.6
Category, generated by a protocategory      A1.1.5
Category, geometric      A1.4.18
Category, Grothendieck      B1.3.1
Category, Hey ting      A1.4.10
Category, ind-small      C4.2.18
Category, indexed      B1.2.1
Category, internal      B2.3.1(a)
Category, Karoubian      A1.1.10
Category, lextensive      B1.5.10 D1.3.6
Category, locally cartesian      A1.2.6
Category, locally cartesian closed      A1.5.3
Category, locally internal      B2.2.1
Category, locally presentable      B4.5.2 D2.3.6
Category, locally small      A1.1.1 B1.3.12
Category, logical      A1.4.1
Category, partial      D3.1.8
Category, positive coherent      A1.4.4
Category, properly cartesian closed      A1.5.1
Category, regular      A1.3.3
Category, simply connected      A1.2.9
Category, sketchable      D2.3.8
Category, slice      A1.1.6
Category, small      A1.1.1
Category, stiff      B1.3.11
Category, strongly connected      A4.6.9 D3.1.7
Category, structured over $\mathcal{B}$      A1.1.5
Category, suitable for $\Sigma$      D4.1.4
Category, syntactic      D1.4.1 D4.2.4 D4.3.4 D4.4.7
Category, well-copowered      A1.4.17
Category, well-powered      A1.4.17 B1.3.14
Centre (of local morphism)      C3.6.2
Characteristic morphism      A1.6.1
Choice, axiom of      D4.5.4
Choice, dependent      D4.5.16
Choice, external      D4.5.4
Choice, internal      D4.5.1(b)
Classifying map (of subobject)      A1.6.1
Classifying topos      B4.2.1(b) D3.1.1
Classifying topos for atomless Boolean algebras      D3.4.12
Classifying topos for cartesian theory      D3.1.1
Classifying topos for coherent theory      D3.1.9
Classifying topos for decidable objects      D3.2.7
Classifying topos for dense linearly ordered objects      D3.4.11
Classifying topos for geometric theory      B4.2.9 D3.1.12
Classifying topos for infinite decidable objects      D3-4.10
Classifying topos for K-finite objects      D3.2.10
Classifying topos for objects      B3.2.9 D3.2.1
Classifying topos for partial equivalence relations on N      C5.2.8(c)
Classifying topos for partial surjections $N\looparrowright N^{N}$      D4.1.9
Classifying topos for propositional theory      B4.2.12
Classifying topos for regular theory      D3.1.4
Classifying topos for subobjects of I      B3.2.10
Classifying topos for subterminal objects      B3.2.11
Classifying topos, Boolean      D3.4.3
Cleavage      B1.3.4
Cleavage, normalized      B1.3.4
Closed subgroup theorem      C5.3.2
Closure (of subtopos)      A4.5.20
Closure operation, universal      A4.3.2
Co-bag of $\mathbb{T}$-models      B4.4.21(b)
Coadjoint retract      B1.1.9
Cocomplete object (in 2-category)      B1.1.16
Cocomplete object (in 2-category), injective      B1.1.16
Cocomplete object (in 2-category), linearly      B1.1.16
Cocomplete object (in 2-category), pointwise      B1.1.16
Coherent category      A1.4.1
Coherent category, Boolean      A1.4.10
Coherent category, positive      A1.4.4
Colocalization      C3.6.19
Comma object      B1.1.4(c)
Comonad, cartesian      A4.2.1
Comonad, idempotent      B1.1.9(c)
Comorphism of sites      C2.3.18
Comparison lemma      C2.2.3
Completeness Theorem for $\lambda$-calculus      D4.2.6
Completeness Theorem for $\mu\lambda E$-caIculus      D4.4.9
Completeness Theorem for $\tau L$-calculus      D4.3.19(b)
Completeness Theorem for $\tau$-calculus      D4.3.11
Completeness Theorem for cartesian logic      D1.4.6 D1.5.1
Completeness Theorem for coherent logic      D1.4.11 D1.5.10
Completeness Theorem for first-order logic      D1.4.11 D1.5.14 D3.1.18
Completeness Theorem for geometric logic      D1.4.11 D3.1.16
Completeness Theorem for regular logic      D1.4.11 D1.5.4
Completeness Theorem, Classical      D1.5.4 D1.5.10 D1.5.14 D3.1.16
Completeness Theorem, conceptual      D3.5.9
Completeness Theorem, functional      D1.3.12 D3.1.3
Composition predicate      A1.1.5
Comprehension scheme      B1.3.12
Comprehensive factorization      B2.5.11
Condition (PCC)      B4.4.4
Cone in sketch      D2.1.1
Cone, discrete      D2.1.1
Cone, lax      B1.1.6
Cone, weighted      B1.1.3
Constant symbol      D1.1.1
context      D1.1.4 D4.4.2
Context, canonical      D1.1.4
Context, suitable      D1.1.4
Continuous G-set      A2.1.6
Continuous G-set, uniformly      A2.1.7
Continuous map (of locales)      C1.2.1
Continuous map (of locales), closed      C3.2.1
Continuous map (of locales), minimal surjective      D4.6.8
Continuous map (of locales), open      C1.5.3
Continuous map (of locales), perfect      C3.2.9
Continuous map (of locales), proper      C3.2.5
Continuous map (of locales), separated      C3.2.9
Continuous map (of locales), triquotient      C3.2.7
Coproduct, $\mathcal{S}$-indexed      B1.4.4
Coproduct, disjoint      A1.4.4
Coproduct, disjoint $\mathcal{S}$-indexed      B1.4.11
Coproduct, quasi-disjoint      A1.5.14
Coproduct, stable $\mathcal{S}$-indexed      B1.4.10
Core (in allegory)      A3.3.1
Coreflexive pair      A1.2.10
Cosieve      A1.6.6 A4.5.2
Cotensor      B1.1.4(b)
Cover      A1.3.2
Coverage      A2.1.9 C2.1.1
Coverage, canonical      C2.1.11
Coverage, chaotic      C2.2.14(a)
Coverage, coherent      A2.1.11(b) C2.1.12(d)
Coverage, dm-      C3.2.18
Coverage, Grothendieck      C2.1.8
Coverage, induced      C2.2.2
Coverage, pre-canonical      C2.1.12(d)
Coverage, regular      A2.1.11(a) C2.1.12(b)
Coverage, rigid      C2.2.18(b)
Coverage, separated      C2.1.11
Coverage, sifted      C2.1.3
Coverage, subcanonical      C2.1.11
Coverage, Zariski      A2.1.11(f) D3.1.11(a)
Covering family      A1.3.2 A2.1.9 C2.1.1
Curry-Howard isomorphism      D4.2.1
de Morgan’s law      D4.6.2
De Morgan’s law, strong      D4.6.6
De Morgan’s law, weak      D4.6.4
Decalage      B2.5.4(b)
Dedekind section      D4.7.4
Definability (in fibration)      B1.3.15
Definability Theorem      D3.5.1
Derivation      D1.3.1
Descent condition      B1.5.2
Descent condition, effective      B1.5.2
Descent data      B1.5.1
Descent morphism      B1.5.5
Diaconescu’s theorem      B3.2.7
Diagram in directed graph      D2.1.1
Diagram in indexed category      B2.3.11
Diagram, constant      B2.5.4(a)
Diagram, lax      B1.1.6
Diagram, weighted      B1.1.3
Diers completion      D3.2.8
Direct image      A4.1.1(a)
Dissolution (of locale)      C1.2.13
Distribution (on topos)      B4.5.8
distributor      B2.7.1
Doctrine      B1.1.11
Domain      C1.1.3
Double coset      D3.4.1
Edwards criterion      C3.4.4
Effectivization      A3.3.10
Eilenberg-Moore object      B1.1.7
Embedding (of structures)      D1.2.10(c)
Embedding (of structures), elementary      D1.2.10(b)
Epimorphism, extremal      A1.3.2
Epimorphism, regular      A1.3.2
Epimorphism, strong      A1.3.2
Equifier      B1.1.4(f)
Equivalence (in 2-category)      B1.1.2
Equivalence (in 2-category), strong      B1.1.2
Equivalence (in allegory)      A3.3.1
Equivalence (of categories)      A1.1.1
Equivalence (of categories), weak      A1.1.1
Equivalence (of theories)      D1.3.7(b)
Equivalence (of theories), Morita      D1.4.9 D1.4.13
Equivalence relation      A1.3.6
Equivalence relation, effective      A1.3.6
Equivalence relation, strong      C2.2.13
Equivalence sieve      C3.4.5
Espace etale      C1.3.3
Etale completion      C5.3.16
Etale morphism      C1.3.3
Etendue      C5.2.4
Excluded middle, law of      D1.3.3
Exponential ideal      A1.5.10
Exponential transpose      A1.5.1
Exponential variety      C5.4.1
Exterior (of subtopos)      A4.5.19
Factorization theorem for locally connected morphisms      C3.3.5
Factorization theorem for pre-geometric morphisms      A4.1.13
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