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

Locale, stably locally compact      C4.1.11
Locale, strongly compact      C3.4.1
Locale, strongly Hausdorff      C1.2.17
Locale, strongly zero-dimensional      D4.5.2(d)
Localic groupoid      C5.2.11
Localic groupoid, algebraically connected      C5.3.7
Localic groupoid, atomic      C5.2.11
Localic groupoid, etale-complete      C5.3.16
Localic groupoid, open      C5.2.11
Localic groupoid, proper      C5.2.11
Localic reflection      A4.6.12
Localization (of cartesian category)      A4.3.1
Localization (of topos)      C3.6.12
Loewenheim-Skolem Theorem      D2.3.10
Logic, $\kappa$ -cartesian      D2.3.6
Logic, $\kappa$ -first-order      D3.1.19
Logic, cartesian      D1.3.4
Logic, classical      D1.3.3
Logic, coherent      D1.3.1
Logic, disjunctive      D1.3.6
Logic, first-order      D1.3.1
Logic, infinitary      D1.3.1
Logic, regular      D1.3.1
Logical category      A1.4.1
Logical functor      A2.1.1
Logos      A1.4.10
Los’s Theorem      D2.4.11
MacNeille completion      C2.5.8(e)
MacNeille section      D4.7.4
Mal’cev operation      D4.2.13
Map (in allegory)      A3.1.3
Martin-Loef type theory      D4.4.1
Measure (on topos)      B4.5.8
Measure (on topos), probability      B4.5.12
Model (of sketch)      D2.1.1(c)
Model (of theory)      B4.2.1(c) D1.2.10(b) D4.1.5
Model (of theory), conservative      D3.2.6
Model (of theory), finitely presented      D2.4.1
Model (of theory), free      D5.3.5
Model (of theory), functionally complete      D3.1.3
Model (of theory), generic      B4.2.1(b) D1.4.5 D3.1.1
Model (of theory), term      C3.6.3(c)
Model (of theory), ultraproduct of      D2.4.11
Modification      B1.1.2
Modular law      A3.1.5
Monad (in 2-category)      B1.1.7
Monad (in 2-category), idempotent      B1.1.9
Monad (in 2-category), KZ-      B1.1.11
Monad (in 2-category), symmetric      B4.5.6
Monoid, free      D5.3.3
Morita equivalence      D1.4.9 D1.4.13
Morita equivalence for localic groupoids      C5.3.1
Morleyization      D1.5.13
Morphism of allegories      A3.2.10
Morphism of diagrams      B2.3.11
Morphism of fibrations      B1.3.6
Morphism of profunctors      B2.7.1
Morphism of sites      C2.3.1 C2.3.7
Morphism of sketches      D2.1.1(b)
Morphism of structures      D1.2.1
Morphism, cartesian      B1.3.3
Morphism, characteristic      A1.6.1
Morphism, descent      B1.5.5
Morphism, effective descent      B1.5.5
Morphism, elementary      D1.2.10(a)
Morphism, etale      C1.3.3
Morphism, fully monic      B1.1.19
Morphism, geometric      A4.1.1
Morphism, horizontal      B1.3.1
Morphism, pre-descent      B1.5.5
Morphism, pre-geometric      A4.1.13
Morphism, prone      B1.3.3
Morphism, supine      B1.3.3
Morphism, vertical      B1.3.1
Name (of relation)      A2.1.1 A3.4.5
Natural number object      A2.5.1
Natural number object, Freyd      D5.1.1
Natural number object, Lawvere      D5.1.1
Natural number object, Peano      D5.1.1
Natural number object, standard      D5.1.7
Natural number object, weak      D4.2.12
Natural transformation, $\mathcal{V}$ -enriched      B2.1.1
Natural transformation, indexed      B1.2.1
Natural transformation, internal      B2.3.1(c)
Natural transformation, lax      B1.1.2
Natural transformation, locally internal      B2.2.1
Natural transformation, pseudo-      B1.1.2
Natural transformation, strong      B2.1.6
Negation (of subobject)      A1.4.13
Nerve (of internal category)      B2.3.2
Nucleus      C1.1.13
Nucleus, closed      C1.1.16(b)
Nucleus, dense      C1.1.16(c)
Nucleus, double-negation      C1. 1.16(c)
Nucleus, fibrewise closed      C1.1.22
Nucleus, fibrewise dense      C1.1.22
Nucleus, flat      C1.1.16(d)
Nucleus, open      C1.1.16(a)
Nucleus, strongly dense      C1.1.22
Nucleus, weakly closed      C1.1.22
Numeral      D5.5.4
Numeral, K-finite      D5.5.9
Object classifier      B3.2.9 B4.2.9 D3.2.1
Object of components      B2.5.5
Object of generators      B3.1.7
Object of morphisms      B2.3.1(a)
Object of objects      B2.3.1(a)
Object, $\bar{K}$ -finite      D5.4.22
Object, $\kappa$ -presentable      D2.3.1
Object, choice      D4.5.5
Object, coarse      A2.6.11
Object, cocomplete      B1.1.16
Object, coherent      D3.3.4
Object, compact      D3.3.2
Object, consistent      D3.4.5
Object, decidable      A1.4.15
Object, decidably well-ordered      D5.1.6
Object, Dedekind-finite      A1.6.10 D5.1.4
Object, exponentiable      A1.5.1
Object, finitely presentable      C4.2.1 D2.3.1
Object, generic      D3.2.1
Object, Higgs      D4.5.10
Object, indecomposable      A1.1.10
Object, internally projective      D4.5.1(b)
Object, irreducible (for coverage)      C2.2.18(a)
Object, Kuratowski-finite      D1.1.7(k) D5.4.1(b)
Object, list      A2.5.15 D4.1.4
Object, natural number      A2.5.1
Object, order able      C5.4.8
Object, power      A2.1.1 A3.4.5
Object, projective      A1.1.10 A1.3.8
Object, quasi-initial      A1.5.14
Object, R-finite      D5.5.12
Object, real number      D4.7.4
Object, separated      A4.3.4
Object, simplicial      B2.3.2
Object, solid      A2.6.6
Object, stable      D3.3.4
Object, strict (initial)      A1.4.1
Object, subterminal      A1.5.10
Object, supercoherent      D3.3.10
Object, supercompact      D3.3.10
Object, thin      A2.6.6
Object, well-ordered      D4.5.9
Object, well-supported      A1.3.8
Opfibration      B1.3.7(a)
Opfibration in 2-category      B4.4.1
Opfibration, discrete      B2.5.1
Oplax functor      B1.1.2
Oplax limit      B1.1.6

Orbital      D5.5.1
Orbital, acyclic      D5.5.3
Orbital, K-finite      D5.5.9
Orbital, Ordered wedge      D4.7.15
Orbital, thick      D4.7.15
Ore condition      A2.1.11(h)
Partial map      A2.4.6 A3.4.10
Partial map, representable      A2.4.6
Partial product      A1.5.7
Partial product, contravariant      B4.4.13
Partial product, covariant      B4.4.13
Partial surjection      A4.6.1
Peano postulates      A2.5.9 D4.3.17(c) D5.1.1
Pierce representation      B4.4.23
Pitts’s Theorem      C2.3.17
Point (of locale)      C1.2.1
Point (of locale), focal      C1.5.6
Point (of topos)      C2.2.12
Poset, complete      B2.3.9
Poset, conditionally complete      D4.7.7
Poset, continuous      C4.1.1(b)
Poset, Dedekind-complete      D4.7.7
Poset, directed      B2.6.2
Poset, DM-separated      D4.7.15
Poset, inductive      D4.5.14
Poset, internal      B2.3.8
Posite      C1.1.16(e)
Positivization      A1.4.5
Power object      A2.1.1 A3.4.5
Power object, weak      A2.6.1
Pre-bound      D3.2.3
Pre-descent condition      B1.5.2
Pre-geometric morphism      A4.1.13
Pre-logos      A1.4.1
Pre-stack      B1.5.2
Preframe      C1. 1.3
Preorder      A1.1.5
Presheaf      A2.1.8 C1.3.1(a)
Presheaf, flat      B3.2.3
Pretopology      A2.1.9
Pretopos      A1.4.8
Pretopos, $\infty$ -      A1.4.19
Pretopos, $\sigma$ -      A1.4.19
Product, $\mathcal{S}$ -indexed      B1.4.2
Profunctor (internal)      B2.7.1
Profunctor (internal), unit      B2.7.2
Profunctor comonad      C4.2.16
Progenitor      B3.1.7
Propositions-as-types paradigm      D4.2.1
Protocategory      A1.1.5
Protomorphism      A1.1.5
Pseudo-complement      A1.4.13
Pseudofunctor      B1.1.2
Pseudofunctor, strictly unital      B1.1.2
Pseudonatural transformation      B1.1.2
Pullback-stability theorem for atomic morphisms      C3.5.12
Pullback-stability theorem for coherent morphisms      C2.4.7
Pullback-stability theorem for connected locally connected morphisms      C3.3.15
Pullback-stability theorem for connected tidy morphisms      C3.4.15
Pullback-stability theorem for exponentiable morphisms      B4.3.5
Pullback-stability theorem for fibrations      B4.4.3
Pullback-stability theorem for hyperconnected morphisms      B3.3.7 C2.4.11
Pullback-stability theorem for local maps      C3.6.7(iv)
Pullback-stability theorem for localic morphisms      B3.3.6
Pullback-stability theorem for locally connected morphisms      C3.3.15
Pullback-stability theorem for open maps      C3.1.11 C3.1.23 C3.1.27
Pullback-stability theorem for proper maps      C3.2.6 C3.2.21
Pullback-stability theorem for tidy morphisms      C3.4.7
Pullback-stability theorem for totally connected morphisms      C3.6.18
Pure-entire factorization      C3.4.13
Quasitopos      A2.6.1
Quasitopos, Grothendieck      C2.2.13
Quasitopos, solid      A2.6.5
Real number object, Cantor      D4.7.12
Real number object, Cauchy      D4.7.12
Real number object, Dedekind      D4.7.4
Real number object, formal      D4.7.5
Real number object, MacNeille      D4.7.4
Real number object, semicontinuous      D4.7.2
Rectangular diagram category      B1.3.12
Recursion data      D5.1.9
Recursive function, partial      D5.1.6
Recursive function, primitive      A2.5.4
Recursor      D4.2.11(a)
Reflection      A1.1.1
Reflector      A1.1.1
Reflector, cartesian      A4.3.1
Reflexive pair      A1.1.2
Regular category      A1.3.3
Regular category, capital      A1.3.8
Regular category, effective      A1.3.6
Regular category, quasi-effective      C2.2.13
Regularization      A1.3.9
Relation      A1.3.6 A2.1.1 A3.1.1
Relation symbol      D1.1.1 D4.1.1
Relation, apartness      D4.7.6
Relation, entire      D4.5.5
Relation, equivalence      A1.3.6
Relation, name of      A2.1.1
Relation, opposite      A3.1.3
Relation, reflexive      A1.3.6
Relation, symmetric      A1.3.6
Relation, transitive      A1.3.6
Ring, indecomposable      B4.4.23
Ring, local      D1.1.7(g)
Ring, reduced      D3.1.11(b)
Ring, separably real-closed local      D4.7.10
Ring, von Neumann regular      D3.1.11(b)
Rule of inference      D1.3.1
Rule of inference of $\lambda N$ -calculus      D4.2.11(b)
Rule of inference of $\lambda$ -calculus      D4.2.2
Rule of inference of $\mu\lambda$ -calculus      D4.4.5
Rule of inference of $\tau$ -calculus      D4.3.1
Rule of inference, cut      D1.3.1(a)
Rule of inference, equality      D1.3.1(b) D4.2.2
Rule of inference, substitution      D1.3.1(a)
Rule of inference, weakening      D1.3.1 (a)
Ryll-Nardzewski’s criterion      D3.4.6
Scone      A2.1.12
Scott topology      C4.1.3
Section, Dedekind      D4.7.4
Section, lower      D4.7.1
Section, MacNeille      D4.7.4
Semilattice      C1.1.3
Semilattice, complete join-      C1.1.3
Semilattice, continuous      C4.1.1(c)
Semilattice, free      C1.1.3 D5.4.9
Semilattice, Heyting      A1.5.11
Semilattice, join-      C1.1.3
Semilattice, meet-      C1.1.3
Sentence      D1.1.3
Separating family      A1.2.4 B2.4.1
Separator      A1.2.4 B2.4.1
Separator, strong      A3.4.10
Sequent      D1.1.5
Sequent calculus      D1.3.1
Sequent, cartesian      D1.1.7(m) D1.3.4
Sequent, coherent      D1.1.5
Sequent, derivable      D1.3.1
Sequent, disjunctive      D1.3.6
Sequent, first-order      D1.1.5
Sequent, geometric      D1.1.5
Sequent, Horn      D1.1.5
Sequent, provable      D1.3.1
Sequent, regular      D1.1.5
Sequent, satisfied in M      D1.2.12(a)
Sheaf for a closure operation      A4.3.4
Sheaf on a locale      C1.3.1(b)
Sheaf on a site      A2.1.9 C2.1.2
Sheaf on a space      A2.1.8

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