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Lavendhomme R. — Basic Concepts of Synthetic Differential Geometry |
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Предметный указатель |
-algebra 305
Abstraction symbol 270
Action of a Lie group 248
Action of a Lie object 191
Adjoint of a left action 250
Adjoint representation 252
Affine automorphism 246
Affine vector field 246
Almost complex connection 229
Almost complex structure 226
Almost Hermitian object 230
Arc of marked surface 117
Axiom, Bunge 59
Axiom, Fermat — Reyes 26
Axiom, general Kock 42
Axiom, integration 19
Axiom, Kock — Lawvere 2
Axiom, Koszul 182
Axiom, Lie-module 182
Axiom, preorder 17
Axiom, Wraith 58
Based vector field 254
Bianchi identity 200
Boundary operator 108
Breadth of a Weil algebra 36
Bunge axiom 59
Category 279
Characteristic function 295
Classical differential form 104
Classical global differential form 184
Coadjoint representation 253
Coequalizer 283
Complex object 227
Connecting map 257
Connecting mapping 163
Connection 143
Connection form 163
Connection on a vector bundle 255
Connection, almost complex 229
Connection, global 145
Connection, linear 192
Connection, pointwise 143
Connection, Riemannian 212
Connection, symmetric 155
Contravariant functor 281
Coproduct 283
Covariant derivation 147
Covariant derivation on a vector bundle 257
Covariant differential 169
Curvature 176
Curvature form 174
De Rham cohomology 116
Degenerate chain 136
Derivation 76
Derivation axiom 182
Derivative 6
Differential 12
Differential form 102
Differential form, classical 104
Differential form, classical global 184
Differential form, integral of a 110
Differential form, singular 102
Differential form, singular global 184
Diffusion 264
Diffusion on a vector bundle 264
Directional derivative 11
Distribution of dimension 99
Epimorphism 282
Equalizer 283
Euclidan vector bundle 66
Euclidean 5
Extensionality 278
Exterior differential 115
Exterior product 124
Fermat — Reyes axiom 26
Finite limit 50
Finitely complete 283
Formula 271
functor 280
General Kock axiom 42
Germ 309
Germ-determined ideal 309
Global connection 145
Global presymplectic structure 216
Global Riemannian structure 216
Good finite limit 52
h-antisymmetric 243
h-gradient 217
h-orthogonal 242
Hadamard's lemma 20
Hamilton equations 267
Hamilton operator 221
Hamiltonian 220
Height of a Weil algebra 36
Hermitian object 230
Hermitian structure 230
Holomorph 229
Homogeneous 15
Infinitesimal n-chain 108
Initial object 283
| Integral of a differential forml 10
Integration axiom 19
Interior product 126
Isomorphism 282
Iterated tangent bundle 87
k-infinitesimally linear object 58
Kaelherian object 232
Killing vector field 244
Kock — Lawvere Axiom 2
Koszul's axiom 182
Left-invariant 240
Lie bracket 73
Lie derivative 76
Lie derivative in the direction of X 236
Lie derivative of a form 128
Lie group 239
Lie module axiom 182
Lie object 182
Lie operator 77
Lie R-algebra 73
Lie, action of a, group 248
Lie, action of a, object 191
Linear connection 192
Liouville 1-form 259
Liouville 2-form 259
Liouville's field 255
Localizing system 293
Locally Hamiltonian 220
Membership relation 270
Micro-square 87
Microcube 87
Microlinear 57
modus ponens 272
Monomorphism 282
Natural transformation 281
Object of line type 302
Operation symbol 270
p-form on a Lie object 187
Parallel transport 164
Pointwise connection 143
Pointwise pre-symplectic structure 216
Pointwise Riemannian structure 211
Poisson bracket 221
Poisson map 247
Poisson object 222
Poisson structure 223
Poisson tensor 224
Poisson vector field 247
Pre-symplectic structure 216
Pre-symplectic, global, structure 216
Predicate calculus 276
Preorder axiom 17
Presheaf 291
PRODUCT 283
Pullback 284
Quasi colimit 52
Reflexive immersed manifold 85
Reflexive object 81
Relation symbol 270
Relations are representable 287
Representable functor 282
Riemannian connection 212
Riemannian structure 211
Riemannian structure on a Lie object 212
Set of zeros of an ideal 309
Sheaf 291
Sheaf w.r. a localizing system 293
Singular differential form 102
Singular global differential form 184
Small object 36
Spectrum 33
Spray 151
Stokes formula 121
Strong difference 92
Subobject 284
Symmetric connection 155
Symplectic structure 220
Tensor product 123
Term 271
Terminal object 283
Theory of -algebras 305
Topos 287
Torsion 171
Torsion form 170
Torsion of an almost complex object 226
Truth values object 278
Truth values object (in a topos) 295
TYPE 270
Variable 270
Varying set 287
Vector bundle 66
Vector field 69
Vector tangent 61
Weil algebra 35
Weil characteristic homomorphism 210
Weil, breadth of a Weil algebra 36
Weil, height of a Weil algebra 36
Well powered 284
Whitney sum 159
Wraith axiom 58
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