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| Johnstone P.T. — Topos Theory |
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| Предметный указатель |
 -category 334
-topos 113
 -torsor 282
Acyclic object 262
Admissible class 206
Algebraic theory 192 195
Almost mono/epi 91
Arithmetic operations 165
Artin, M. xii 112
Associated sheaf functor 11 15 90
atom 258
Atomic category 257
Baer, R. 261
Barr, M. xiii xvi 18 41 249 254 257
Beck condition 32 134 342
Beck, J. 3 32 106
Benabou, J. xiv xv xvi 58 59 63 108 152 156 173 203 334 343
Bernays, P. xix
Bidense morphism 91
Boileau, A. 319
Boolean algebra 137
Boolean algebra, topos 138
Boolean-valued model 322
Borceux, F. 146
Bourn, D. xix
Brook, T.G. 303
Bunge, M.C. 255 329
Calculus of fractions 6
Cardinal, finite 173
Cartan, H. xi 271
Category of fractions 6
Category, atomic 257
Category, balanced 27
Category, cartesian closed 23
Category, closed span 54
Category, enriched 335
Category, filtered 66
Category, Galois 285
Category, Grothendieck 73
Category, internal 47
Category, locally closed 54
Category, locally internal 335
Category, small 1
Category, syntactic 243
Celeyrette, J. xiv 334 345
Choice, axiom of 141
Choice, axiom of, implicit 143
Classifying map 23
Classifying map, topos 117 203
Closure 77
Cohen, P.J. 324 329
Cohomology group 261
Cohomology group with cosupports 294
Cohomology group, Cech 268 269
Cole, J.C. xv 206 303 316
Colimit functor 52
Complement 138
Conduche, F. 57
Continuum Hypothesis 324
Conway, J.H. xix 214
Coste, M. 319
Countable chain condition 325
Covering family 12
Covering family, sieve 13
Day, B.J. 54
Decidable object 162
Dedekind real number 211
Deligne, P. xii xv 213 240 242
Diaconescu, R., xv 112 113 120 123 141 249 294
Diagram, constant 51
Diagram, internal 49
Diagram, lax 107
Diagram, representable 51
Direct image 26
Discrete (op)fibration 50
Disjoint coproduct 15
Duskin, J.W. 279 282
Eilenberg, S. xii 3 262 279
Element 39
Element, generic 39
Element, global 39
Engenes, H. 45
Enriched category 335
Epimorphic family 225
Epimorphic family, sieve 20
Equivalence relation 16
Equivalence relation, effective 16
Etale morphism 21
Etale morphism, topos 22
Etendue 255
Evaluation map 31
Extension (of a formula) 154
Exterior {of a topology) 102
Fakir, S. 106
Fibration, discrete 50
Field of fractions 215
Field, geometric 215
Field, residue 215
Filter 319
Filtered category 66
Filterpower 320
Flabby 264
Fourman, M.P. 152 155 220 223 319
Freyd, P. xii xiv xviii xix 101 166 168 222 251 314 331 332 340
Funayama, N. 253
Functor, cofinal 74
Functor, continuous 225
Functor, direct image 26
Functor, fringe 112
Functor, internal 48
Functor, inverse image 26
Functor, locally internal 335
Functor, logical 26
Functor, pullback 35
Functor, strong 172
Fundamental group 288 290
G-set 25
G-set, continuous 262
G-torsor 117
Gabriel, P. 6
Galois category 285
Generators, object of 121
Generators, set of 16
Generic element 39
Generic element, object 117 182
Generic element, point 230
Generic element, subobject 24
Generic element, T-model 204 246
Geometric language 199
Geometric morphism 26
Geometric morphism, bounded 121
Geometric morphism, essential 26
Geometric morphism, inclusion 103
Geometric morphism, surjection 103
Geometric theory 201
Giraud, J. xii xv 15 16 120 123 279
Glenn, P. 282
Glueing 109
Godement, R. xi 264 266
Goedel, K. xv xix 243
Gray, J.W. 48
Grillet, P.A. xiii
Grothendieck category 73
Grothendieck categoryб pretopology 12
Grothendieck categoryб topology 13-
Grothendieck categoryб topos 15
Grothendieck, A. xi xii 12 15 48 73 84 234 239 260 262 285 288 336
Hakim, M. xv 208
Heller, A. 87
Henkin, L. xv 243
| Heron, A. xii
Heyting algebra 137
Higgs, D. 44
Hilbert, D. 295
Hochster, M. 248
Image (of geometric morphism) 104
Image (of morphism in a topos) 40
Inaccessible element 256 331
Inclusion (of toposes) 103
Inclusion (of transitive objects) 304
Integral domain 215
Interior (of a topology) 102
Internal category 47
Internal category, diagram 49
Internal category, full subcategory 58 340
Internal category, functor 48
Internal category, presheaf 49
Internal category, profunctor 59
Internalization 58
Internally complete (category) 53
Internally complete, (internal poset) 147
Internally projective 143
Interpretation (of language) 153 200
interval 118
Inverse image 26
Isbell, J.R. 163
Johnstone, P.T. xv 21 87 189
Jonsson, B. 222
Joyal, A. xv xvi 97 98 118 157 159 201 203 210 245
Kan extension 56
Kan, D.M. 56
Kaplansky, I. 220
Kelly, G.M. xii 40
Kennison, J.F. 209
Kock, A. xiv xviii 43 159 296 298 322
Kripke — Joyal semantics 157
Kripke, S. 157 159
Kuratowski, C. 78 296
Kuratowski-fmite 296
Kuratowskian ordered pair 164
Lambek, J. 93
Language, geometric 199
Language, Mitchell — Benabou 153
Lattice 136
Lattice, Brouwerian 137
Lattice, distributive 136
Lattice, Stone 162
Lawvere, F.W. xii xiii xiv xv xvii 23 24 28 35 54 76 84 92 100 104 139 165 192 302 320 322 324 329 334
Lax colimit 108
Lax colimit, diagram 107
Lecouturier, P. 296 298
Leray spectral sequence 263
Leray, J. xi 26
Lesaffre, B. 193
Lindenbaum A. 34
Linton, F.E.J. 3
Local ring 198
Locally constant 133 285
Locally internal category 335
Locally internal category, tensored over 342
Locally split 143
Loewenheim, L. 228
Logical functor 26
Lubkin, S. xii
Mac Lane, S. xvi 1 262 279
Makkai, M., xv 243
Mikkeisen, C.J. xiv 31 34 148 190 296 298 300 304 322
Mitchell — Benabou language 153
Mitchell, B. xii
Mitchell, W. xv 121 123 151 152 303 316
Model (of theory) 192 201
Model (of theory), boolean-valued 322
Moore, J.C. 3
Morphism classifier 184
Morphism, bidense 91
Morphism, central 281
Morphism, etale 21
Morphism, geometric 26
Morphism, local 199
Mostowski, A. 304 313
Mulvey, C.J. 220
Natural number object 165
Natural transformation of geometric morphisms 26
Natural transformation, internal 72
Object classifier 117 182
Object of epimorphisms 157
Object of generators 121
Object of isomorphisms 157
Object of morphisms 47
Object of objects 47
Object, acyclic 262
Object, coherent 233
Object, compact 232
Object, decidable 162
Object, essential 255
Object, flabby 264
Object, generic 117 182
Object, locally constant 133 285
Object, natural number 165
Object, normal 287
Object, open 94
Object, partially transitive 311
Object, separated 81
Object, simplicial 48
Object, stable 233
Object, transitive 304
Opfibration, discrete 50
Opfibration, split 73
Osius, G. xv 152 156 157 303 311 316
Pare, R. 31 33 198 334 339 345
Partial map 28
Partially transitive 311
Penon, J. xix 54 58 334 335
Point (of a topos) 224
Poset, antisymmetric 137
Poset, directed 67
Poset, internal 48
Poset, internally complete 147
Poset, well-ordered 159
Power-object 43
Presheaf 1 9
Presheaf, constant 9
Presheaf, flat 113
Presheaf, internal 49
Presheaf, representable 1
Presheaf, separated 10 14
Pretopology 12
Pretopos 238
Profinite completion 284
Profinite completion group 283
Profunctor, internal 59
Profunctor, left flat 119
Profunctor, symmetric 274
Profunctor, Yoneda 61
Provably equivalent 243
Pseudo-Boolean algebra 137
Pseudo-point 227
Pullback functor 35
Rank (of a functor) 134
Rattray, B.A. 93
Real number object, Cauchy 218
Real number object, Dedekind 212
Reflexive pair 3
Reid, M.A. xx
Relation, equivalence 16
Relation, extensional 304
Relation, inductive 304
Reyes, G.E. xv 201 243 245
Robinson, A. 322
Roos, J.E. 254
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