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

Factorization theorem for tidy morphisms      C3.4.15
Factorization theorem, closed inclusion-totally connected      C3.6.17(d)
Factorization theorem, comprehensive      B2.5.11
Factorization theorem, direct image-inverse image      A4.1.12
Factorization theorem, hyperconnected-localic      A4.6.5
Factorization theorem, open inclusion-local      C3.6.3(f)
Factorization theorem, pure-entire      C3.4.13
Factorization theorem, surjection-inclusion      A4.2.10
Fibration      B1.3.4
Fibration in 2-category      B4.4.1
Fibration of sites      C2.5.6
Fibration, associated split      B1.3.10
Fibration, cartesian      B1.4.1
Fibration, cloven      B1.3.4
Fibration, continuous      C2.5.6
Fibration, discrete      B1.3.11 B2.5.1
Fibration, interval      C2.1.13
Fibration, locally small      B1.3.12
Fibration, satisfying (PCC)      B4.4.4
Fibration, split      B1.3.4
Fibration, stiff      B1.3.11
Fibration, well-powered      B1.3.14
Field      D1.1.7(h)
Field, coherent      D1.1.7(h)
Field, residue      D4.7.9
Filter, completely prime      C1.2.1
Filter, neighbourhood      C1.2.1
Filterpower      A2.1.13
Filterquotient construction      A2.1.13
Finite cardinal      A2.5.14 D5.2.1
Finite cardinal, generic      A2.5.14
Finite object, $\bar{K}$ -      D5.4.22
Finite object, Dedekind-      A1.6.10 D5.1.4 D5.2.9
Finite object, Kuratowski-      D1.1.7(k) D5.4.1(b)
Finite object, Russell-      D5.5.12
Finite object, Sierpinski-      D5.4.1
Fixset      C1.1.13
Fixset, dense      C1.1.16(c)
Formula      D1.i.3 D4.1.3
Formula in context      D1.1.4
Formula, $\mathbb{T}$ -complete      D3.4.13
Formula, atomic      D1.1.3 D4.1.3
Formula, cartesian      D1.1.7(m) D1.3.4
Formula, closed      D1.1.3
Formula, coherent      D1.1.3
Formula, complete      D3.4.13
Formula, disjunctive      D1.3.6
Formula, first-order      D1.1.3
Formula, geometric      D1.1.3
Formula, Horn      D1.1.3
Formula, provably equivalent      D1.3.7(a)
Formula, regular      D1.1.3
Formula, well-formed      D1.1.3
Frame      A3.2.2(b) C1.1.1
Frame, coherent      C2.4.3
Frame, consistent      C2.4.9
Frame, Giraud      B4.5.1
Frame, internal      C1.6.1
Frame, nontrivial      C2.4.9
Frame-valued set      A3.3.13 C1.3.3
Frame-valued set, complete      C1.3.6
Free topos      D4.3.14(a)
Free topos with natural number object      D4.3.19(d)
Frobenius reciprocity      A1.3.3 A1.5.8
Function symbol      D1.1.1 D4.1.1
Functional completeness      D1.3.12 D3.1.3 D4.2.10
Functional extension (of theory)      B4.2.7(a)
Functor between 2-categories      B1.1.2
Functor, $\kappa$ -continuous      D2.3.4
Functor, $\kappa$ -Heyting      D3.1.19
Functor, $\mathcal{S}$ -continuous      B1.4.13
Functor, $\mathcal{V}$ -enriched      B2.1.1
Functor, 2-initial      B3.4.11
Functor, accessible      B3.1.12
Functor, bicartesian      D5.1.8
Functor, biseparated      C2.2.13
Functor, cartesian      A1.2.1
Functor, cartesian closed      A1.5.2
Functor, cocontinuous (between sites)      C2.3.18
Functor, cofinal      B2.5.12
Functor, coherent      A1.4.4
Functor, conservative      A1.1.1
Functor, continuous (between sites)      C2.3.1
Functor, continuous (indexed)      B1.4.13
Functor, cover-creating      C3.5.10
Functor, cover-preserving      C2.3.1
Functor, cover-reflecting      C2.3.18
Functor, direct image      A4.1.1(a) C1.4.3
Functor, essentially surjective      A1.1.1
Functor, faithful      A1.1.1
Functor, final      B2.5.12
Functor, finitely covering      D3.5.7
Functor, flat      C2.3.7
Functor, full on subobjects      D3.5.6
Functor, Heyting      A1.4.10
Functor, indexed      B1.2.1
Functor, initial      B2.5.11
Functor, internal      B2.3.1(b)
Functor, inverse image      A4.1.1(a) C1.4.1
Functor, lax      B1.1.2
Functor, left exact      A1.2.1
Functor, locally internal      B2.2.1
Functor, logical      A2.1.1
Functor, monadic      A1.1.2
Functor, regular      A1.3.3
Functor, separated      A2.6.4(d) C2.1.2
Functor, strict      B1.1.2
Functor, strong      B2.1.4
Functor, sub-cartesian-closed      C3.1.1
Functor, sub-logical      C3.1.1
Functor, tripleable      A1.1.2
Fundamental Theorem of topos theory      A2.3.2
G-set      A2.1.4
G-set, continuous      A2.1.6
G-set, effective      B3.2.4(b)
G-set, transitive      B3.2.4(b)
G-set, uniformly continuous      A2.1.7
G-torsor      B3.2.4(b)
Generating family      A1.2.4
Generator      A1.2.4
Geometric category      A1.4.18
Geometric category, $\infty$ -positive      A1.4.19
Geometric construct      B4.2.5
Geometric construct, coherent      B4.3.8
Geometric morphism      A4.1.1(a)
Geometric morphism, $\mathcal{S}$ -essential      B3.1.1
Geometric morphism, $\mathcal{S}$ -indexed      B3.1.2
Geometric morphism, atomic      C3.5.1
Geometric morphism, Beck-Chevalley      C2.4.16
Geometric morphism, bounded      B3.1.7
Geometric morphism, closed      C3.2.3
Geometric morphism, connected      C1.5.7
Geometric morphism, descent      C5.1.1
Geometric morphism, embedding      A4.2.9
Geometric morphism, entire      B4.4.21(a)
Geometric morphism, essential      A4.1.5
Geometric morphism, hyperconnected      A4.6.3
Geometric morphism, hyperlocal      B4.4.19
Geometric morphism, inclusion      A4.2.9
Geometric morphism, lax descent      C5.1.8
Geometric morphism, local      C3.6.1
Geometric morphism, localic      A4.6.1
Geometric morphism, locally connected      C3.3.1
Geometric morphism, minimal surjective      D4.6.8
Geometric morphism, open      C1.5.4 C3.1.7
Geometric morphism, partial      A4.1.13
Geometric morphism, pre-descent      C5.1.1
Geometric morphism, proper      C3.2.12(a)
Geometric morphism, pure      C3.4.12
Geometric morphism, separated      C3.2.12(b)

Geometric morphism, skeletal      D4.6.9
Geometric morphism, stably closed      C3.2.26
Geometric morphism, surjection      A4.2.6
Geometric morphism, tidy      C3.4.2
Geometric morphism, totally connected      C3.6.16
Geometric morphism, weak Beck—Chevalley      C2.4.16
Geometric quotient      B4.2.7(b)
Geometric theory      B4.2.7(c) D1.1.6
Geometric theory, dualizable      B4.3.2
Geometric theory, prepositional      B4.2.12 D1.1.7(m)
Geometric transformation      A4.1.1(b)
Giraud frame      B4.5.1
Giraud frame, symmetric      B4.5.4
Giraud’s Theorem      B3.3.4 B3.3 11 C2.2.8
Giraud’s Theorem, little      C2.1.11
Gleason cover      D4.6.8
Glued topos      A2.1.12
Glueing construction      A2.1.12
Godel’s Incompleteness Theorem      D4.3.19(d)
Graph of morphism      A3.1.3
Graph, directed      D2.1.1
Graph, undirected      D3.2.7
Grothendieck construction      A1.1.7 B1.3.1
Grothendieck coverage      C2.1.8
Grothendieck topology      A2.1.9
Grothendieck topos      C2.2.9
Groupoid, internal      B2.3.12(c)
Groupoid, localic      C5.2.11
Heine-Borel Theorem      D4.7.4
Heyting algebra      A1.5.11
Heyting algebra, irreducible      A2.6.4(e)
Heyting category      A1.4.10
Heyting semilattice      A1.5.11
Higgs object      D4.5.10
Hyperconnected-localic factorization      A4.6.5
Ideal for coverage      C1.1.16(e) C2.3.21
Ideal in poset      B3.2.4(d) C1.1.3
Ideal, exponential      A1.5.10
Ideal, maximal      D4.6.14
Ideal, prime      D4.6.14
Ideal, proper      D4.6.14
Idempotent      A1.1.8
Idempotent (in 2-category)      B1.1.9
Idempotent monad      B1.1.9
Idempotent monad, associated      A4.3.11
Idempotent, split      A1.1.8
Idempotent, symmetric      A3.3.2
Identifier      B1.1.4(e)
Image      A1.3.1
Image, direct      A4.1.1
Image, inverse      A4.1.1
Inclusion (geometric)      A4.2.9
Indexed category      B1.2.1
Indexed category, cartesian      B1.4.1
Indexed category, complete      B1.4.2
Indexed category, essentially small      B2.3.4
Indexed category, locally small      B1.3.12
Indexed category, well-powered      B1.3.14
Indexing, canonical      B1.2.2(c)
Indexing, naive      B1.2.2(a)
Inductive completion      C4.2.1
inserter      B1.1.4(d)
Interior (of subtopos)      A4.5.19
Internal category      B2.3.1(a)
Internal category, connected      B2.5.6
Internal category, discrete      B2.3.12(a)
Internal category, filtered      B2.6.2(a)
Internal category, indiscrete      B2.3.4
Internal category, weakly filtered      B2.6.2(b)
Internal full subcategory      B2.3.5
Internal groupoid      B2.3.12(c)
Internal language      D1.3.11 D4.1.8
Internal poset      B2.3.8
Internal poset, complete      B2.3.9
Internal poset, conditionally complete      D4.7.7
Internal poset, Dedekind-complete      D4.7.7
Internal poset, directed      B2.6.2
Internal poset, DM-separated      D4.7.15
Internal site      C2.4.1
Internalization      C1.6.1
Interpolation property      C4.1.2 C4.2.15
Interpretation (in structure)      D1.2.3 D1.2.6 D4.1.5
Interpretation (in structure), Brouwer-Heyting-Kolmogorov      D1.2.2
Interpretation (in structure), Tarski      D1.2.1
Interval (in poset)      C2.1.13
Inverse image      A4.1.1(a)
Inverter      B1.1.4(e)
Iterator      D4.1.2(ix)
Joyal’s Lemma      C4.1.15
Kan extension      A4.1.4
Kan extension, internal      B2.3.20
Knaster-Tarski Theorem      D4.1.10
Kock-Zoeherlein monad      B1.1.11
KZ-monad      B1.1.11
L-valued matrix      A3.2.2(b)
L-valued set      A3.3.13
Language, first-order      D1.1.1
Language, higher-order      D4.1.1
Language, internal      D1.3.11 D4.1.8
Lattice, continuous      C4.1.1(c)
Lattice, distributive      C1.1.3
Lattice, stably continuous      C4.1.10
Lawvere-Tierney topology      A4.4.1
Lax functor      B1.1.2
Lax limit      B1.1.6
Lax limit, normalized      C2.3.15(d)
Lax pullback      B1.1.4(c)
Leibniz equality      D4.3.2
Limit power cardinal      A2.1.2
Limit, conical      B1.1.3
Limit, indexed      B1.1.3
Limit, lax      B1.1.6
Limit, weighted      B1.1.3
Lindenbaum algebra      D1.4.14
Lindenbaum algebra for Dedekind sections of $\mathbb{Q}$       D4.7.4
Lindenbaum algebra for injections $A\rightarrowtail\mathbb{N}$       C1.2.9
Lindenbaum algebra for paradoxical open cover of [0,1]      D4.7.13
Lindenbaum algebra for partial surjections $\mathbb{N}\looparrowright\mathbb{N}^{N}$       D4.1.9
Lindenbaum algebra for surjections $\mathbb{N}\twoheadrightarrow A$       C1.2.8
List object      A2.5.15 D4.1.4
Local character condition      C2.1.8
Local homeomorphism      A1.2.7 C1.3.2 C3.3.4
Local operator      A4.4.1
Local operator, closed      A4.5.3
Local operator, dense      A4.5.20
Local operator, double-negation      A4.5.9
Local operator, open      A4.5.1
Local operator, pullback      A4.5.14(e)
Local operator, quasi-closed      A4.5.21
Locale      C1.2.1
Locale, $T_{U}$ -      C1.2.17
Locale, coherent      C2.4.3
Locale, compact      C1.5.5
Locale, connected      C1.5.7
Locale, discrete      C1.6.4
Locale, exponentiable      C4.1.9
Locale, extremally disconnected      C1.5.10 D4.6.3(b)
Locale, Hausdorff      C1.2.17
Locale, injective      C4.1.6
Locale, internal      C1.6.1
Locale, local      C1.5.6
Locale, locally coherent      C4.1.13
Locale, locally compact      C4.1.7
Locale, locally connected      C1.5.8
Locale, locally metastably compact      C4.4.7
Locale, locally stably compact      C4.1.11
Locale, open      C3.1.16
Locale, regular      C1.2.17
Locale, second countable      D4.5.2(d)
Locale, spatial      C1.2.3 C1.6.5

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