SGA — English Translation › SGA 4 — Topoi and Sites

SGA 4-I — Terminological Index

Translated from the cleaned OCR transcription of the image-only SGA 4-I scan. References are OCR-derived navigation aids and should be checked against the scan when precision matters.

[PDF p. 534]

Terminological Index

• Accessible (functor) — I 9.2
• Accessible (object) — I 9.3
• Closure of a subtopos — IV 9.4.8
• Artinian (set) — I 0, I 11.6
• Artinian (object) — I 8.12.6
• Bicovering (morphism, family) — II 5.2
• Cartesian, cocartesian — II 10.1
• $U$-category — I 1.1
• Category of points of a topos — IV 4.6.3
• Filtered category — I 2.7
• Pseudo-filtered category — I 2.7
• Cofinal (functor, subcategory) — I 8.1.1
• Cogenerating (subcategory) — I 7.1
• Comparison (lemma of) — III 4.1
• Constant, essentially constant (Ind-object) — I 8.4
• Covering (sieve) — II 1.1.1
• Covering (morphism, family) — II 5.2
• Covering (family) — II 1.2
• Sieve — I 4.1
• Dominant (morphism of topoi) — IV 8.8
• Universally effective epimorphic (family) — II 2.5
• Epimorphic (family) — I 10.3
• Universally strict epimorphic (sieve, family) — II 2.5
• Universally epimorphic (family) — I 10.3
• Epimorphism, strict epimorphism — I 10.3
• Effective epimorphism — I 10.3
• Essential (morphism, point) — IV 7.6
• Spread — IV 9.8.2
• Exterior of a subtopos — IV 9.4.8
• Sheaf with values in a category $D$ — II 6.1
• Sheaf of sets — II 2.1
• Sheaf of morphisms — IV 10.2
• Gluing sheaf — IV 9.6
• Cardinal filtration — III 9.2
• Cocontinuous functor — III 2.1

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• Conservative functor — I 6.1
• Continuous functor — III 1.1
• Gluing functor — IV 9.3.5
• Left exact, right exact, exact functor — I 2.4
• Fiber functor — IV 4.6.3
• Faithful functor — I 6.1
• Extension-by-zero functor — IV 11.3.1
• Restriction-of-scalars functor — IV 11.1.4
• Section functor — IV 4.3.6
• Fiber functors — IV 6.0
• Boundary of a subtopos — IV 9.4.8
• Generating, cogenerating (family) — I 7.1
• Generating, cogenerating (subcategory) — I 7.1, I 7.9
• Generating (family … of a site) — II 3.0.1
• Topologically generating (family … of a site) — II 3.0.1
• Generalization of a point — IV 4.2.2
• Big topos of a topological space — IV 4.10, IV 2.5
• Direct image of modules — IV 13.2.1
• Image of a morphism of topoi — IV 9.1.7
• Inverse image of a subtopos — IV 9.1.6
• Inverse image of an induced topos — IV 5.10
• Inverse image of modules — IV 13.2.2
• Inaccessible (cardinals) — I 0
• Inaccessible (cardinals) — I 11.5
• Inclusion (morphism of) — IV 5.2
• Ind-adjoint — I 8.11.2
• Ind-object — I 8
• Strict Ind-object — I 8.12.1
• Ind-representable (functor) — I 8.2
• Induced (topos) — IV 5.2
• Interior of a subtopos — IV 9.4.8
• Inductive limit — I 2.3.1
• Universal inductive limit — I 2.5
• Projective limit — I 2.1
• $U$-projective limit — I 2.2.1
• Finite projective and inductive limit — I 2.3.1
• Local (relation of nature) — IV 8.2
• Localization (functor of) — IV 5.4
• Localization (morphism of) — IV 5.2

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• Monomorphic, monomorphism — I 10.4
• Morphism of topoi — IV 3.1
• Morphism of sites — IV 4.9
• Morphisms of ringed topoi — IV 13.1
• Morphisms of locally ringed topoi — IV 13.9
• Initial object — II 4.5
• Open of a topos — IV 8.2
• Small (set, group, ring, category, etc.) — I 4.0
• $U$-small (set) — I 1.0
• Embedding — IV 9.1.1
• Closed embedding — IV 9.3.5
• Open embedding — IV 9.2.1
• Geometric point — IV 13.9
• Points of a topos — IV 6.0
• Represented presheaf — I 1.3.3
• Representable presheaf — I 1.4.1
• Presheaves of sets — I 1.2
• Pretopology — II 1.3
• Pro-adjoint — I 8.11.5
• Pro-objects — I 8 to I 8.10
• Pro-representable (functor) — I 8.12
• Pro-representable (functors) — I 8.10.10
• Projector — I 10.6
• Extension by the empty object — III 5.3
• Squarable (arrow, morphism) — I 10.7
• Quotient, effective strict quotient, universal quotient — I 10.8
• Refinement — II 1.1
• Equivalence relation — I 10.9
• Local equivalence relation — IV 9.8.3
• Effective, universally effective equivalence relation — I 10.10
• Weil restriction — IV 5.2
• Restriction of a sheaf — IV 5.4, III 5.3
• Separated (presheaf) — II 2.1
• Site — II 1.1.5
• $U$-site — II 3.0.2
• Locally ringed site — IV 13.9
• Sober (topological space) — IV 4.2.1
• Disjoint sum — II 4.5

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• Subobject, strict subobject — I 10.11
• Subtopos — IV 9.1.1
• Complementary subtopoi — IV 9.1.13
• Complemented subtopos — IV 9.1.13
• Closed subtopos — IV 9.3.5
• Locally closed subtopos — IV 9.4.9
• Open subtopos — IV 9.2.3
• Specialization of a point — IV 4.2.2
• Stable under descent — IV 8.2
• Strictly Ind-representable — I 8.12.1
• Support of a group or of a section — IV 9.3.5
• r-structure — IV 9.8.3
• Support, cosupport — IV 8.5
• Topology — II 1.1
• $U$-topology — II 3.0.2
• Canonical topology — II 2.5
• Discrete topology — II 1.1.4
• Coarse and chaotic topology — II 1.1.4
• Induced topology — III 3.1
• Topos — IV 1.1
• $U$-topos — IV 1.1
• Ringed topos — IV 11.1.1
• Classifying topos — IV 2.3, IV 2.4, IV 2.5
• Equivalent topoi — IV 3.4
• Finite topos — IV 9.1.12
• Initial, final topos — IV 2.2
• Rigid topos — IV 9.8.2 b)
• Universe — I 0
• Universe — I 11.1
• Universe (axiom of universes) — I 11.4
• Neighborhood — IV 6.8