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| MacLane S. — Categories for the working mathematician |
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| Предметный указатель |
Product, smash 185
Product, tensor 124 159
Product, tensor of objects 113
Product, tensor, category 36
Product, tensor, diagram 1 69
Projections 1 69
Projections of comma category 48
Projections of product 1 36 69 70
Projections of product category 36
Projective object 114
Proper class 23
Pseudo-filtered category 212
PTT-Beck 150
Pullback 48 ex. 71
Pullback, square 71 199
Pushout 65
Quasi-inverse 83
Quotient, field of 56
Quotient, field of object 122 198
Quotient, field of topology 129 155
Rank of word 162
Reflection 87 89
Reflection of colimits 150
Reflection of isomorphisms 150
Reflective subcategory 89
Reflector 89
Regular arrow 19
Regular arrows 21
Relations 26 174
Relative category 180
Relaxed morphism 160
Replacement axiom 23
Representability 60 ff.
Representability, formal criterion for 231
Representability, formal criterion for theorem 118
Representation 60 ff.
Representation, left regular 170
Resolution 177 ft.
Retraction 19
Right adjoint 2 79 82 230
Right adjoint, right inverse 129
Right adjunct 79
Right cancellable 19
Right exact sequence 197
Right inverse 19
Right Kan extension 232 233
Ring, small 25
Root 76 (notes)
SAFT 126
Satisfaction of identities 12U
Scheme, diagram 10 49
Section (= right inverse) 19
Semigroup 140 142 176
Semigroup, free 140
Sentence 31
Sequence, right exacl 197
Sequence, short exact 196 198
Sets 11
Sets, based 26
Sets, category of small 12 62
Sets, cogenerating 123
Sets, directed 207
Sets, filtered 207
Sets, function 40
Sets, generating 123
Sets, graded 120
Sets, linearly ordered 176
Sets, metacategory ol 8
Sets, pointed 26
Sets, simplicial 12 174
Sets, small 12 22 62
Sets, solution 116 ff. 231
Sets, underlying 120
Sheaf 35
simplex 174 ff.
Simplex, affine 174
Simplex, singular 176
Simplicial category 12 174
Simplicial object 174
Simplicial set 174
Singular, chain complex 176
Singular, homology 176
Singular, simplex 176
Skeleton (of a category) 91
Small complete category 105 106
Small group 22
Small pointed set 26
Small ring 25
Small set 22
Small topological space 25
Smash product 185
Snake lemma 202
Solenoid, p-adic 107
Solution set (condition) 116 ff.
Source 7
Space, compact Hausdorff 154
Space, compactly generated 181
Space, Euclidean vector 216
Space, function 181
Space, Hausdorff 131
Space, Kelley 181
Space, loop 185
Space, path 186 ex.
Space, topological 12 25 153 181
Space, vector 25 56 77
Span an object 123
Split 19 145
Split, coequalizers 146
Split, epi 19
Split, fork 145
Split, idempoient 20
Split, monic 19
Square, adjoint 101 ex
Square, cartesian 71
| Square, cocartesian 66
Square, pullback 71 199
Statement, atomic 31
Stone — Cech compactification 127
Strict monoidal category 171
Structure map of algebras 139
structure map of T algebras 137
Subcategory 15
Subcategory, codense 242
Subcategory, dense 241 ff.
Subcategory, final 213
Subcategory, full 15
Subcategory, reflective 89
Subdivision category 220
Subobject 122
Sum, direct 191
Sum, fibered 66
Super comma category 111 ex.
Super-comma category 111 ex.
Supernatural transformation 215
Surjective 19
Surjective, monotone function 173
Suspension 185
Symmetric monoidal category 180
System, algebraic 120
T algebras 136
T-algebras 136 ff.
TARGET 7
Tensor product 124 159 222
Terminal object 20 73
Terminology, table of 247
Theorems, Beck’s characterizing algebras 147
Theorems, Beck’s precise tripleability 150
Theorems, comparison for algebras 138
Theorems, construction of free monoids 168
Theorems, formal criterion for existence of adjoints 230 244
Theorems, Freyd’s adjoint functor 117 231
Theorems, Fubini 226
Theorems, Kan extensions as a coend 237
Theorems, Kan extensions as a pointwise limit 233
Theorems, parameter for ends and limits 224 ff.
Theorems, representability 118
Theorems, special adjoint functor 124
Theorems, special initial object 124
Topological spaces 25
Topological spaces, category of 1 12 128
Topological spaces, compactly generated 181
Topological spaces, small 25 128
Topology, compact open 181
Topology, Hausdorff 131
Topology, identification 129
Topology, quotient 129 155
Topology, subspace 128
Transformations 16 99
Transformations, components of 16
Transformations, composite 102
Transformations, conjugate natural 98
Transformations, dinatural 214
Transformations, extranatural 215
Transformations, natural 16
Transformations, supernatural 215
Transformations, universal natural 38
Triad 134
Triangular identities 83
Triple 134
Tripleable (=monadic) 139
Two-dimensional category 44 102
Two-sided inverse 14
Underlying functor 14
Underlying sets 26 120
union 21 122
UNIT 85
Unit law 8 134
Unit of adjunction 81
Unit of Kan extension 237
Unit of monad 134
Universal 36
Universal arrow 24 55 58 61
Universal arrows 8 55 58 231
Universal cone 67
Universal element 57
Universal monoid 157 171
Universal natural transformation 39
Universal property 2
Universal wedge 219
Universal, weak arrow 231
Universality 59
Universality of Kan extensions 245
Universe 12 22
Urysohn lemma 128 ex.
Variable, bound 31 224
Variable, dummy 215
Variable, free 31
Variable, free, of integration 219
Variety of algebras 120
Vector spaces 25 56 77
Vertical composite 42 102
Watt’s Theorem 127
Weak universal arrow 231
Weak universal arrows 231
wedge 185—215
Wedge, universal 219
Well-powered category 126
Word 141
Word, binary 161
Yoneda, embedding 243
Yoneda, functor 61 62
Yoneda, lemma 61 246
Zermelo — Fraenkel axioms 23
Zero arrows 20 74 187 190
Zero, arrow 20 74 187 190
Zero, map 188
Zero, morphism 188
Zigzag 203
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