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| Adamek J., Herrlich H., Stecker G.E. — Abstract and Concrete Categories - The Joy of Cats |
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| Предметный указатель |
Regular monomorphism vs. section 7.59
Regular monomorphism vs. strict monomorphism 12A
Regular monomorphism vs. topos 28F
Regular monomorphism, composition of 7J 10M 14I 28.6
Regular monomorphism, first factor 14I
Regular projective object 9E
Regular quotient object 7.84
Regular subobject 7.77
Regular subobject vs. intersection 11K
Regular wellpowered category 7.82
Regular wellpowered category vs. category with separator or co-separator 7.89
Regular wellpowered categoryvs. construct 7.88
Regular wellpowered categoryvs. wellpowered category 7.83
Regularly algebraic category 23.35 ff
Regularly algebraic category vs. adjoint functor 23.38
Regularly algebraic category vs. regular factorization 23.39
Regularly algebraic category vs. uniquely transportable functor 23.38
Regularly algebraic category, characterization theorem for 23.38
Regularly algebraic functor 23.35 ff 23E 23M
Regularly algebraic functor, decomposition theorem for 24.2
Regularly algebraic functor, implies associated monad is regular 24.1
Regularly algebraic functor, implies comparison functor is a regular epireflective embedding 24.1
Regularly monadic category, vs. regular factorization 20.30
Regularly monadic functor 20.21 ff 20L
Regularly monadic functor is regularly algebraic 23.36
Regularly monadic functor vs. monadic functor 20.35
Regularly monadic functor vs. solid functor 26.4
Regularly monadic functor, characterization theorem for 20.32
Regularly monadic functor, composition of 24.2
Regularly monadic functor, detects colimits 20.33
Regularly monadic functor, detects extremal co-wellpoweredness 20.31
Relation, congruence, = congruence relation 11.20
Relational category 28H
Represent M-partial morphisms 28.1
Representable extremal partial morphisms 28.19
Representable functor 6.9 6K
Representable functor preserves limits 13.9
Representable functor preserves mono-sources 10.7
Representable functor preserves monomorphisms 7.37
Representable functor vs. adjoint functor 18C
Representable functor vs. duality 10N
Representable functor vs. free object 8.23
Representable M-partial morphisms, vs. topological category 28.12
Representable partial morphisms vs. final sinks are reducible 28.15
Representable partial morphisms vs. topological category 28.15
retract 7.24
Retract in an isomorphism-closed full reflective subcategory 7.31
Retract vs. injective object 9.5
Retract, absolute 9.6
Retraction 7.24 ff
Retraction is epimorphism 7.42
Retraction is pullback stable 11.18
Retraction is regular epimorphism 7.75
Retraction preserved by all functors 7.28
Retraction preserved by products 10.35
Retraction reflected by full, faithful functor 7.29
Retraction vs. (E, M)-structured category 14.9
Retraction vs. product 10.28
Retraction vs. projection morphism 10.27
Retraction vs. quotient morphism 8.12
Retractionas monomorphism means isomorphism 7.36
Retractionpreserved and reflected by equivalence functor 7.47
Right adjoint, = adjoint 19.11
Right inverse of a morphism, vs. left inverse 3.10
Russell's paradox 2.2 2.3 3.51 3L
Satisfaction of an implication, = e-injective 16.11 16.12
Satisfaction of topological (co-)axiom 22.1 22.6
Scheme, = domain of a diagram 11.1
Section 7.19 ff 7E
Section as epimorphism is isomorphism 7.43
Section is (regular) monomorphism 7.35 7.59
Section preserved by all functors 7.22
Section preserved by products 10.35
Section reflected by full, faithful functor 7.23
Section vs. embedding 8.7
Section vs. equivalence functor 7.47
Section vs. intersection 11K
Section vs. monomorphism 7P
Section vs. pullback 11H
Self-adjoint endofunctor 19G
Self-dual concept 3.7. See also Pulation square
Self-dual properties for functors 3.43
Semifinal arrow, for a structured sink 25.8 25C
Semifinal solution, for a structured sink 25.7 25C
Separating set 7.14
Separating set vs. concretizable category 7Q
Separator 7.10 ff
Separator vs. (co)wellpoweredness and (co)complete- ness 12.13
Separator vs. bicoreflective subcategory 16.4
Separator vs. faithful hom-functor 7.12
Separator vs. topological category 21.16 21.17
Separator, category with, is regular (co-)wellpowered 7.89
Separator, extremal 10.63
Set is a (small) class 2.2
Set, constructions that can be performed with sets 2.1
Set, morphism class of small category is a set 3.45
Set, separating, = separating set 7.14
Set, underlying, = underlying set see Forgetful functor
Set-indexed family of sets 2.2
Set-indexed source 10.2
Set-valued functor vs. hom-functor 6.18
Set-valued functor vs. natural transformation 6.18
Singleton-morphism 28.11
Sink 10.62 ff
Sink, costructured 17.4
Sink, final 10.63 28.15
Sink, natural 11.27
Situation, adjoint, = adjoint situation 19.3 ff
Skeleton of a category 4.12—4.15 4I
Small category 3.44. See also Fibre-small
Small category is a set 3.45
Small class 2.2
Small conglomerate 2.3
Small object-free category 3.55
Small source 10.2
Smallest containing E-reflective subcategory, = E-reflective hull 16.20 16.21
Smallest injective extension 9.20
Smallest injective extension vs. minimal injective extension 9G
Smallness of hom-class condition see Object-free category
Solid concrete category 25.10 ff
Solid concrete category is almost topologically algebraic 25.18 25.19
Solid concrete category vs. (co)complete category 25.15 25.16
Solid concrete category vs. Mac Neille completion 25G
Solid concrete category vs. subcategory of topological category 26.2
Solid concrete category vs. topological category 25J
Solid concrete category, characterization theorems 25.19 25I
Solid concrete category, structure theorem 26.7
Solid construct, need not be topologically algebraic nor strongly cocomplete 25.17
Solid functor 25.10 ff
Solid functor detects colimits and preserves and detects limits 25.14
Solid functor is almost topologically algebraic 25.18 25.19
Solid functor is faithful and adjoint 25.12
Solid functor preserves extremal monomorphisms 25.21
Solid functor vs. adjoint functor 25.12 25.19
Solid functor vs. detection and preservation of limits 25.18 25.19
Solid functor vs. essentially algebraic functor 26.3
Solid functor vs. faithful functor 25.12
Solid functor vs. full reflective embedding 26.1
Solid functor vs. monadic functor 25F
Solid functor vs. regularly monadic functor 26.4
Solid functor vs. topological functor 26.1 26.3 26.4
Solid functor vs. topologically algebraic functor 25D 25E 26.1
Solid functor, composite of topological and essentially algebraic functors 26.3
Solid functor, composite of topological and regularly monadic functors 26.3
Solid functor, composite of topologically algebraic functors 26.1
Solid functor, composition of 25.13
Solid functor, topologically algebraic functor is 25.11
Solution set condition 18.12
Source 10.1 ff
Source, codomain of 10.1
| Source, composite of 10.3
Source, domain of 10.1
Source, empty 10.2
Source, initial, = initial source 10.41 10.57
Source, natural 11.3
Source, notation for 10.2 10.4
Source, set-indexed 10.2
Source, small 10.2
Source, structured, w.r.t. a functor 17.1
Split coequalizer 20.14
Split epimorphism, = retraction 7.24 ff
Split fork 20.14
Split monomorphism, = section 7.19 ff
Square, commutes 3.4
Square, pulation 11.32 11.33 11Q
Square, pullback, = pullback square 11.8 ff
Stability under pullbacks 11.17 28.13
Stable epimorphism 11J
Stable epimorphism vs. adjoint functor 18I
Statement, dual, = dual statement 3.7
Stone-functor 3.20(11)
Strict monomorphism 7D
Strict monomorphism vs. other types of monomorphisms 7.76
Strict monomorphism vs. pullback 11H
Strict monomorphism vs. regular monomorphism 12A
Strong fibre-smallness 26D
Strong monomorphism 7.76 14C
Strongly cocomplete category 12.2
Strongly cocomplete category is (Epi, ExtrMono-Source)-category 15.17
Strongly cocomplete category vs. (co)complete category 12.5 12I 12N 12O
Strongly complete category 12.2
Strongly complete category is (E, M)-structured 14.21
Strongly complete category vs. (co)complete category 12.5 12I 12N 12O
Strongly complete category vs. (E, M)-category 15.25 15.26
Strongly complete category vs. free monad & varietor 20.59
Strongly fibre-small concrete category 26.5
Strongly generating structured arrow 25.4
Strongly generating structured arrow is generating 25.5
Strongly limit-closed subcategory, vs. epireflective subcategory 16L
Strongly n-generating object 20H
Structure, factorization: for morphisms 14.1 ff
Structure, factorization: for sources 15.1 ff
Structure, factorization: w.r.t. a functor 17.3 ff
Structured 2-source, factorizations of 17F
Structured arrow 8.15
Structured arrow, (extremally) generating, vs. (extremal) epimorphism 8.36
Structured arrow, equivalence for 26.5
Structured arrow, generating, = generating structured arrow 8.15
Structured arrow, isomorphic 8.19 8.34
Structured arrow, strongly generating 25.4 25.5
Structured arrow, universal 8.30
Structured arrow, w.r.t. a functor 8.30
Structured source, notation for 17.2
Structured source, self-indexed 17.2
Structured source, w.r.t. a functor 17.1
Subcategory 4.1 ff
Subcategory of a functor-costructured category vs. topological category 22.8
Subcategory of a functor-structured category vs. (M-) topological category 22.3 22.4 22.9
Subcategory vs. identities 4A
Subcategory, algebraic, = algebraic subcategory 23.32
Subcategory, bireflective 16.1 16.3
Subcategory, colimit-closed 13I
Subcategory, colimit-dense, = colimit-dense subcategory 12.10
Subcategory, concrete 5.21 ff
Subcategory, coreflective, = coreflective subcategory 4.25 16.1
Subcategory, definable by topological (co-)axioms 22.1 22.3 22.4 22.6
Subcategory, dense 12D
Subcategory, E-equational 16.16
Subcategory, E-reflective 16.1
Subcategory, epireflective 16.1
Subcategory, extremally epireflective 16.1
Subcategory, finally closed 21.29
Subcategory, finally dense 10.69 10.69
Subcategory, full 4.1(2) ff
Subcategory, implicational 16.12
Subcategory, initially closed 21.29
Subcategory, initially dense 10.69
Subcategory, isomorphism-dense 4.9
Subcategory, limit-closed 13.26 13.27 13I 13J
Subcategory, limit-dense 12E
Subcategory, M-initially closed, vs. concretely E-reflec- tive subcategory 22.9
Subcategory, monadic, conditions for 20.19
Subcategory, monoreflective 16.1
Subcategory, nonfull 4.3(3)
Subcategory, of subcategories 4G
Subcategory, reflective, = reflective subcategory 4.16 16.1
Subcategory, regular epireflective 16.1
Subcategory, simultaneously reflective and coreflective 4E
Subcategory, topological, = topological subcategory 21.29 ff
Subconstruct 5.21
Subconstruct of a functor-structured construct, vs. monotopological construct 22.10
Subconstruct of Set vs. concretely cartesian closed construct 27.16
Subobject 7.77 ff
Subobject vs. M-subobject 16.8
Subobject, extremal, = extremal subobject 7.77
Subobject, initial, = initial subobject 8.6
Subobject, intersection of 11.23
Subobject, non-isomorphic 7K
Subobject, order on 7.79
Subobject, regular, = regular subobject 7.77
Subset 2.1. See also Power set
Swell epimorphism 7.76 15A
Swell separator 19K
T-algebra 5.37
T-algebra, category of 20.4 5G
T-algebra, category of, closed under the formation of mono-sources 20.11
T-algebra, category of, three-step construction 20.6
T-homomorphism 5.37
T-space 5.40 5H
Taut lift theorem 21.28
Terminal category 3.3(4)
Terminal object 7.4
Terminal object uniqueness 7.6
Terminal object vs. product 10.20 10.30 10H
Terminal object vs. pullback square 11.13
Terminal object vs. weak terminal object 12.9
Terminal, weakly terminal set of objects 12F
Thin category 3.26
Thin category vs. faithful functor 3.29 3G
Thin quasicategory 3.51
Topological (co-)axiom 22.6
Topological axiom 22.1
Topological characterization theorems, external 21.21
Topological characterization theorems, internal 21.18
Topological concrete category 21.7 ff
Topological concrete category is fibre-complete 21.11
Topological concrete category vs. (co)completeness 21.16 21.17
Topological concrete category vs. (E, M)-category 21.14
Topological concrete category vs. (E, M)-factorization 21.16 21.17
Topological concrete category vs. co-wellpoweredness 21.16 21.17
Topological concrete category vs. concretely cartesian closed subcategory 27.15
Topological concrete category vs. concretely reflective subcategory 21.32
Topological concrete category vs. coseparator 21.16 21.17
Topological concrete category vs. discrete object 21.11
Topological concrete category vs. extremal morphism 21.13
Topological concrete category vs. final lift 21.34
Topological concrete category vs. finally dense subcategory 21.32
Topological concrete category vs. has function spaces 27.22
Topological concrete category vs. indiscrete object 21.11 21.35
Topological concrete category vs. initial lift 21.34
Topological concrete category vs. initial subobjects 21.35
Topological concrete category vs. initially closed subcategory 21.30 21.31
Topological concrete category vs. injective object 21.21
Topological concrete category vs. lift of an adjoint situation 21.28
Topological concrete category vs. representable (M-)partial morphisms 28.12 28.15
Topological concrete category vs. separator 21.16 21.17
Topological concrete category vs. solid category 25J
Topological concrete category vs. subcategory of a functor-(co)structured category 22.3 22.4 22.8
Topological concrete category vs. wellpoweredness 21.16 21.17
Topological concrete category, characterization 21C
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