Johnstone P.T. — Sketches of an Elephant: A Topos Theory Compendium :: Электронная библиотека попечительского совета мехмата МГУ

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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.

Аннотация:

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:

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

Sheaf, G-equivariant      A2.1.11(c)
Sheafification      A4.4.4
Shift (of simplicial object)      B2.5.4(b)
Sierpinski topos      B3.2.11
Sierpiriski cone      A2.1.12 C3.6.3(f)
Sierpiriski space      A2.1.12 C1.1.4
Sieve      A1.6.6 A4.5.5 C2.1.3
Sieve, closed      A2.1.10
Sieve, connected      C3.3.10
Sieve, covering      C2.1.3
Sieve, dm-      C3.2.18
Sieve, effective-epimorphic      C2.1.11
Sieve, equivalence      C3.4.5
Sifted colimit      A1.2.12
Sifted coverage      C2.1.3
Signature      D1.1.1 D4.1.1
Signature, $\lambda N$ -      D4.2.11 (a)
Signature, $\lambda$ -      D4.2.1
Signature, $\mu\lambda$ -      D4.4.2
Signature, $\tau L$ -      D4.3.16
Signature, $\tau$ -      D4.3.1
Signature, canonical      D1.3.11 D4.1.7
Signature, first-order      D1.1.1
Signature, higher-order      D4.1.1
Signature, propositional      D1.1.7(m)
Simplicial identities      B2.3.2
Simplicial object      B2.3.2
Simplicial object, 2-truncated      B3.4.11
Simplicial topos      B3.4.11
Singleton (in frame-valued set)      C1.3.6
Singleton map      A2.2.2
Site      A2.1.9 C2.1.1
Site of definition      C2.2.15
Site, atomic      C3.5.8
Site, consistent      C2.4.8
Site, essentially small      C2.2.3
Site, internal      C2.4.1
Site, local      C3.6.3(d)
Site, locally connected      C3.3.10
Site, small      C2.1.1
Site, standard      A2.1.11(a) C2.1.11
Site, syntactic      D3.1.1
Sketch      D2.1.1(a)
Sketch, $\sigma$ -coherent      D2.2.9
Sketch, coherent      D2.1.2(g)
Sketch, colimit      D2.1.2(b)
Sketch, coproduct      D2.1.2(c)
Sketch, disjunctive      D2.1.2(e)
Sketch, finitary      D2.1.2(d)
Sketch, finite limit      D2.1.2(b)
Sketch, finite product      D2.1.2(b)
Sketch, geometric      D2.1.2(h)
Sketch, inductive      D2.1.2(c)
Sketch, limit      D2.1.2(b)
Sketch, linear      D2.1.2(a)
Sketch, mixed      D2.1.2(d)
Sketch, product      D2.1.2(b)
Sketch, projective      D2.1.2(b)
Sketch, regular      D2.1.2(f)
Slice category      A1.1.6
Sobrification      C1.2.3
Sorgenfrey plane      D4.5.2(e)
sort      D1.1.1 D4.1.1
Soundness Theorem      D1.3.2 D4.2.3 D4.3.3 D4.4.6
Source-target predicate      A1.1.5
Space, $T_{D}$ -      C1.2.5
Space, Choquet      A2.6.4(b)
Space, coherent      D3.3.14
Space, extremally disconnected      C1.5.10
Space, Fhkihet      A2.6.4(c)
Space, injective      C4.1.6
Space, local      C1.5.6
Space, sober      C1.2.3
Span (in a category)      A3.3.8
STACK      B1.5.2
Stone algebra      D4.6.1
Strength (of functor)      B2.1.4
Structure (for signature)      D1.2.1 D4.1.4 D4.4.3
Subcategory, definable      B1.3.16
Subcategory, dense      C4.2.18 D2.3.2(iii)
Subcategory, dense (for coverage)      C2.2.1
Subcategory, full      A1.1.1
Subcategory, internal full      B2.3.5
Subcategory, reflective      A1.1.1
Subcategory, replete      A1.1.1
Subclosure      C1.2.5
Subfibration      B1.3.16
Subfibration, definable      B1.3.16
Sublocale      C1.2.5
Sublocale, closed      C1.2.6(b)
Sublocale, complemented      C1.2.11
Sublocale, dense      C1.2.6(c)
Sublocale, fibrewise closed      C1.2.14
Sublocale, fibrewise dense      C1.2.14
Sublocale, open      C1.2.6(a)
Submersion      C1.6.7
Subobject      A1.3.1
Subobject classifier      A1.6.1
Subobject classifier, weak      A2.6.1
Subobject, closed      A4.3.2
Subobject, complemented      A1.4.10
Subobject, dense      A4.3.2
Subobject, effective      C3.4.5
Subobject, generic      A1.6.1
Subobject, negation of      A1.4.13
Subobject, widespread      A1.6.11
Subquotient      A4.6.1
Substitution (in formal language)      D1.1.4
Substitution property      D1.2.4 D1.2.7 D4.1.6
Substructure      D1.2.10(c)
Subtopos      A4.3.9
Subtopos, Boolean      A4.5.21
Subtopos, closed      A4.5.3
Subtopos, closure of      A4.5.20
Subtopos, dense      A4.5.20
Subtopos, exterior of      A4.5.19
Subtopos, geometric      A4.3.9
Subtopos, interior of      A4.5.19
Subtopos, logical      A4.3.9
Subtopos, open      A4.5.1

Subtopos, quasi-closed      A4.5.21
Superdense      C1.5.2
Support of an object      A1.3.8
Supports split      D4.5.1(a)
Surjection (geometric)      A4.2.6
Surjection-inclusion factorization      A4.2.10
Syntactic category for $\lambda$ -theory      D4.2.4
Syntactic category for $\mu\lambda$ -theory      D4.4.7
Syntactic category for $\tau$ -theory      D4.3.4
Syntactic category for cartesian theory      D1.4.1
Syntactic category for coherent theory      D1.4.10
Syntactic category for first-order theory      D1.4.10
Syntactic category for geometric theory      D1.4.10
Syntactic category for regular theory      D1.4.10
tabulation      A3.1.1 A3.2.3
Tensor (in 2-category)      B1.1.4(b)
Tensor condition      B4.4.5
Term (in formal language)      D1.1.2 D4.1.2
Term (in formal language) in context      D1.1.4
Term (in formal language), $\lambda$ -      D4.2.1
Term (in formal language), closed      D1.1.3
Term constructor      D4.1.2
Term declaration      D4.4.2
Theory      B4.2.1(a) D1.1.6
Theory of objects      B4.2.4(a) D3.2.1
Theory over S      B4.2.1(a)
Theory, $\aleph_{0}$ -categorical      D3.4.7
Theory, $\lambda$ -      D4.2.2
Theory, $\mu\lambda$       D4.4.4
Theory, $\sigma$ -coherent      D2.2.9
Theory, $\tau L$ -      D4.3.16
Theory, $\tau$ -      D4.3.3
Theory, algebraic      D1.1.7(a) D5.3.1
Theory, cartesian      D1.1.7(m) D1.3.4
Theory, coherent      B4.3.8 D1.1.6
Theory, complete      D3.4.7
Theory, disjunctive      D1.3.6
Theory, equivalent      D1.3.7(b)
Theory, first-order      D1.1.6
Theory, geometric      B4.2.7(c) D1.1.6
Theory, Horn      D1.1.6
Theory, internal algebraic      D5.3.9
Theory, model-complete      D3.4.9
Theory, prepositional      B4.2.12 D1.1.7(m)
Theory, regular      D1.1.6
Topological group, coherent      D3.4.1
Topological group, nearly discrete      A2.1.6
Topological group, pro-discrete      A2.1.6
Topology, Grothendieck      A2.1.9
Topology, Lawvere-Tiemey      A4.4.1
Topos      A2.1.1
Topos, $\mathcal{S}$ -indexed      B3.1.2
Topos, 2-valued      A2.1.13
Topos, atomic      C3.5.1
Topos, bounded over $\mathcal{S}$       B3.1.7
Topos, classifying      B4.2.1(b) D3.1.1
Topos, coherent      D3.3.1
Topos, compact      C3.2.12(a)
Topos, defined over S      B3.1.1
Topos, exponentiable      B4.3.1 C4.4.1
Topos, free      D4.3.14(a) D4.3.19(d)
Topos, glued      A2.1.12
Topos, Grothendieck      C2.2.9
Topos, grouplike      C3.6.9
Topos, Hausdorff      C3.2.12(b)
Topos, having enough points      C2.2.12
Topos, hyperlocal      B4.4.19
Topos, injective      C4.3.1
Topos, Jonsson-Tarski      A2.1.11(i)
Topos, local      C3.6.2
Topos, locally decidable      C5.4.1
Topos, locally orderable      C5.4.8
Topos, measure      B4.5.8
Topos, quasi-injective      C4.3.9
Topos, regular      D3.3.1
Topos, Schanuel      A2.1.11(h)
Topos, Sierpinski      B3.2.11
Topos, simplicial      B3.4.11
Topos, standard      D5.1.7
Topos, strongly compact      C3.4.1
Topos, symmetric      B4.5.4
Topos, totally connected      C3.6.16
Topos, weak      A2.1.1
Topos, Zariski      A2.1.11(f)
Torsor      B3.2.3
Torsor, $\kappa$ -      D2.3.3
TYPE      D1.1.1 D4.1.1
Type constructor      D4.1.1
Type declaration      D4.4.2
Type, basic      D4.1.1
Type, dependent product      D4.4.1
Type, dependent sum      D4.4.1
Type, equality      D4.4.2(g)
Type, function      D4.1.1
Type, list      D4.1.1
Type, Mal’cev      D4.2.15
Type, power      D4.1.1
Type, product      D4.1.1
Type, unit      D4.4.2(f)
Ultrapower      A2.1.13
Ultraproduct      D2.4.11
Union (of subobjects)      A1.4.1
Union (of subobjects), effective      A1.4.3
Unit (in allegory)      A3.2.8
Universal closure operation      A4.3.2
Universal closure operation, proper      A4.4.2
Universal closure operation, strict      A4.4.2
Variable      D1.1.2
Variable, bound      D1.1.3
Variable, free      D1.1.3
Wavy arrow      C4.2.12
Way below      C4.1.1(a)
Weak adjoint      B1.1.8
Weak equivalence      A1.1.1
Weak equivalence of localic groupoids      C5.3.12
Weak subobject classifier      A2.6.1
Weak topos      A2.1.1
Weakening Property      D1.2.4
Wff      D1.1.3
Yoneda profunctor      B2.7.2
Zorn’s Lemma      D4.5.14

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