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| Pareigis B. — Categories and functors |
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| Предметный указатель |
Functor, adjoint functor theorem 105 110 113
Functor, algebraic 137 139 145
Functor, bi- 39
Functor, category 10 221
Functor, cocontinuous 86
Functor, constant 77 79
Functor, continuous 86
Functor, contravariant 7
Functor, covariant 7
Functor, endo- 62
Functor, evaluation 43 45 46
Functor, exact 179
Functor, faithful 44 115 116
Functor, forgetful 8 129
Functor, full 44 115 116
Functor, full faithful 115 117
Functor, halfexact 180
Functor, image of a 24
Functor, isomorphic 18
Functor, leftexact 180 222
Functor, monadic 68 139 140
Functor, multi- 39
Functor, power set 50
Functor, product 55
Functor, projection 39
Functor, representable 10 11 14 40 47 105
Functor, representable functor theorem 109
Functor, representable sub- 105
Functor, representation 44 116 235
Functor, rightexact 180
Gabriel 2 158
Generator 110 111 141 202 245
Generator, pro- 211
Generator, set of 110
Generator, со- 110 112 203 213 245
Goedel 2 247 254 255
Grothendieck 2 158
Grothendieck category 181 182 188
Grothendieck condition 181
Group 3 6 125 126 127 146
Group homomorphism 4
Group, abelian 4
Group, affine algebraic 155
Group, algebraic theory of 125 126 155
Group, algebraic theory of commutative 155
Group, analytic 155
Group, category of finite 16
Group, commutator factor 148
Group, divisible abelian 14 18 148 163
Group, finite abelian 156
Group, homotopy 155
Group, ordered abelian 244
Group, quasi- 145
Group, semi- 145
Group, sub- 21 50
Group, topological 155
Group, torsion 74
Group, torsionfree abelian 74 156
Groupoid 101 104
H-object 145
Halfexact functor 180
Hausdorff topological space 8 15 18 74 114
Hausdorff topological space, compact 74 114
Hausdorff topological space, normal 74 114
Hilton 120
Hoelder 174 176
Homomorphism, algebra- 126
Homomorphism, connecting 243
Homomorphism, group- 4
Homomorphism, insertion 156
Homomorphism, module- 4
Homomorphism, theorem 142 164
Homotopy 5
Homotopy group 155
Hull, injective 195 198
Ideal, nilpotent left 217
Idempotent 190
Identity 2 10
Identityof n-th order 125
Image 34 165 253
Image of functor 24
Image, counter- 34 35 97
Image, epimorphic 34
Image, monomorphic со- 35
Image, со- 34 35 165
Indecomposable object 190
Induced topology 49
Inductive limit 81
Infimum 81
Initial object 22
Injection 33 78
Injective cogenerator 203 213
Injective extension 198
Injective extension, minimal 198
Injective extension, smallest 198
Injective hull 195 198
Injective map 14
Injective object 195
Injective object, relatively 141
Insertion homomorphism 156
Integral domain 115 148
Intersection 33 34 97 171 249
Intersection, со- 34
Inverse limit 81 88
Inversely connected category 60
Isomorphic categories 18
Isomorphic functors 18
Isomorphic morphisms 17 25
Isomorphic objects 17
Isomorphism 14 17
Isomorphism, anti- 19
Isomorphism, creation of 69
Isomorphism, natural 18
Isomorphism, theorems 144 172 173
Jordan algebra 147 149
Jordan algebra, module 147
Jordan algebra, ring 147
Jordan — Hoelder theorem 174 176
Kan 51 108
Kernel 28 163
Kernel, difference 26 81—86 163
Kernel, difference со- 26 28 70 81 163
Kernel, pair 86 141
Kernel, со- 28 163
Kleisli 62 136
Krull 190 193 202 208
Large diagram 79
Large diagram, category 79
Large subobject 197
Largest essential extension 198
Lattice modular 240
Lattice of quotient objects 170
Lattice of subobjects 170
Lawvere 2 120
Left adjoint functor 51 91
Left exact functor 180 222
Left ideal, nilpotent 217
Left root 81
Left zero morphism 22
Length of composition series 174
Length of object 177
Length, object of finite 177
Lie algebra 147 149
Lie algebra, module 147
Lie algebra, ring 146
LIMIT 51 77 81 89 91 97
Limit, direct 81 88
Limit, exact direct 185
Limit, filtered 88
Limit, filtered со- 88
| Limit, inductive 81
Limit, inverse 81 88
Limit, projective 81
Limit, со- 77 78 81 91
Linton 120
LocaIIy arcwise connected space 74
Local ring 190 202
Locally connected space 74
Locally cosmall category 22
Locally noetherian category 206
Locally small category 21 112
Loop 146
M-object 145
Matlis 208
Matrix of homomorphisms 162
Matrix ring, full 219
Maximal condition for chains 21
Maximal essential extension 198
Maximal subobject 21
Metatheorem 240 242
Metatheoremof class formation 251
Minimal condition for chains 21
Minimal injective extension 198
Minimal subobject 21
Mitchell 242
Modular lattice 240
Module 4 147
Module homomorphism 4
Module, bi- 147
Module, cocompact 245
Module, compact 245
Module, finitely generated 205
Module, Jordan 147
Module, Lie 147
Module, relatively projective 196
Monad 61 62
Monad, со- 62
Monadic functor 68 139 140
Monoid 55 56 62 145
Monoid, ring 56 149
Monomorphic coimage 35
Monomorphic equivalence relation 99
Monomorphism 14 87
Monomorphism, equivalent 20
Monomorphism, relatively split 141
Moore 62
Morita 158 210 213 217
Morphism 1 150
Morphism of algebraic theories 121
Morphism of diagrams 25
Morphism, antiiso- 19
Morphism, auto- 17
Morphism, category 25
Morphism, endo- 17
Morphism, endomorphism ring 163
Morphism, epi- 14
Morphism, iso- 14 17
Morphism, isomorphic 17
Morphism, matrix of 161
Morphism, mono- 14 87
Morphism, zero 22 23
Msp 253
Msp, continuous 5
Msp, dense continuous 15
Msp, injective 14 253
Msp, order preserving 3
Msp, pointed 3
Msp, pointed continuous 5
Msp, surjective 14 253
Multifunctor 39
n-ary operation 125
Natural isomorphism 18
Natural numbers 6
Natural transformation 6 9
Nilalgebra 148
Nilpotent algebra 148
Nilpotent element 192
Nilpotent ideal 217
Nine lemma see Three-by-three lemma
Noetherian category 21
Noetherian category, locally 206
Noetherian object 21 206
Noetherian power set 21
Noetherian ring 206
Nonunit 190
Normal hausdorff space 74 114
Normal quotient object 28
Normal subgroup 50
Normal suboboject 28
Numbers, natural 6
Object 1
Object of finite length 177
Object, artinian 21
Object, cogroup 151
Object, coirreducible 208
Object, compact 204
Object, decomposable 190
Object, difference quotient 28
Object, difference sub- 28
Object, final 22 86
Object, finite projective 210
Object, finitely generated 204
Object, Hopf 145
Object, indecomposable 190
Object, initial 22
Object, injective 195
Object, isomorphic 17
Object, large sub- 197
Object, lattice of sub- 170
Object, maximal sub- 21
Object, minimal sub- 21
Object, multiplicative 145
Object, noetherian 21 206
Object, normal quotient 28
Object, normal sub- 28
Object, order of sub- 21
Object, projective 141 195
Object, quotient 20 21
Object, relatively free 141
Object, relatively injective 141
Object, relatively projective 141
Object, representing 11 47
Object, simple 174
Object, sub- 20
Object, transfinitely generated 205
Object, zero 22
Open set 5
Operation, n-ary 125
Order identity of n-th 125
Order of subobjects 21
Order preserving map 3
Ordered abelian group 244
Ordered set 3 6
Ordered set, pre- 81
Pair of adjoint functors 51
Pointed category 23
Pointed continuous map 5
Pointed map 3
Pointed set 3
Pointed topological space 5
Polynomial algebra 149 156
Polynomial algebra, generalized 156
Power class 21
Power class, со- 21 22
Power set 21
Power set, artinian 21
Power set, functor 50
Power set, noetherian 21
Preequivalence relation 101
Preordered set 81
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