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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 |
Injective hull 9.16
Injective hull for finitary varieties 16J
Injective hull vs. enough injectives 9D
Injective hull, existence 9C
Injective hull, uniqueness 9.19
Injective hull, w.r.t. a class of morphisms 9.22
Injective morphism vs. initial morphism 8B
Injective object 9.1
Injective object in CAT, vs. topological category 21.21
Injective object in topological construct 28A
Injective object is an absolute retract 9.7
Injective object preserved by product 10.40
Injective object vs. essential extension 9.15
Injective object vs. maximal essential extension 9F
Injective object vs. reflective subcategory 9.25
Injective object vs. retract 9.5
Injective object, characterization 9B
Injective object, terminal object is 9.4
Injective object, w.r.t. a class of morphisms 9.22
Injective, enough 9.9 15H
Injectivity class 9.26
Insertion of generators 19.4
Intersection of subobjects 11.23
Intersection of subobjects as pullback 11F
Intersection of subobjects vs. (E, M)-structured category 14.15
Intersection of subobjects vs. (Epi, ExtrMono)-structured category 14.19
Intersection of subobjects vs. isomorphism 11.25
Intersection of subobjects vs. limit 11.25
Intersection of subobjects vs. regular subobject & section 11K
Intersection of subobjects, closure under the formation of 11.26
Intersection of subobjects, existence 12.1
Intersection, of a family of sets 2.1
Inverse functor, unique determination 3.25
Inverse image, of a subject 11.19
Inverse limit 11.4
Inverse of a morphism 3.8
Inverse of a morphism, uniqueness 3.11
Inverse of a morphism, “is equivalent to”, is equivalence relation on categories 3.34
Inverse of a morphism, “is isomorphic to” is an equivalence relation on categories 3.25
Inverse of an isomorphism, notation 3.12
Iso-transformation 6.5
Isomorphic categories 3.24 3.25
Isomorphic categories vs. equivalent categories 3.35
Isomorphic objects 3.15
Isomorphic objects, yields equivalence relation on the object class 3.16
Isomorphic structured arrows 8.19 8.34
Isomorphic, concretely 5.12
Isomorphic, naturally 6.5
Isomorphic, “is isomorphic to” is an equivalence relation on categories 3.25
Isomorphism 3.8 ff 3F
Isomorphism functor 3.24
Isomorphism functor is isomorphism in CAT 3.51
Isomorphism functor, closed under composition 3.30
Isomorphism in a category, vs. isomorphic objects 3.15
Isomorphism vs. (E, M)-category 15.5
Isomorphism vs. coequalizer 7.70
Isomorphism vs. epimorphism 7.43 7.66
Isomorphism vs. equalizer 7.54
Isomorphism vs. extremal monomorphism 7.66
Isomorphism vs. final morphism 8.14
Isomorphism vs. identity morphism 3.13
Isomorphism vs. initial morphism 8.14
Isomorphism vs. intersection 11.25
Isomorphism vs. monomorphism 7.36
Isomorphism vs. product source 10.26
Isomorphism vs. retraction 7.36
Isomorphism vs. section 7.43
Isomorphism, composite of, is an isomorphism 3.14
Isomorphism, concrete 5N
Isomorphism, creation 13.35 13M
Isomorphism, functor is isomorphism iff full, faithful, and bijective on objects 3.28
Isomorphism, functors need not reflect 3.22
Isomorphism, Galois 6.26
Isomorphism, inverse is an isomorphism 3.14
Isomorphism, is 1-product 10.20
Isomorphism, natural 6.5
Isomorphism, non-concrete 5B
Isomorphism, preserved and reflected by equivalence functor 7.47
Isomorphism, preserved by functors 3.21
Isomorphism, preserved by products 10.35
Isomorphism, reflection of 13.35 13F
Isomorphism-closed (full) subcategory 4.9 4B
Isomorphism-closed full subcategory, vs. limit-closed 13.27
Isomorphism-dense full subcategory 4.9 4.10 4.12
Isomorphism-dense functor 3.33
Kernel 7C
Kernel vs. pullback 11E
Kleisli category 20.39 20B
Large category 3.44
Large class 2.2
Largest essential extension 9.20
Left adjoint, = co-adjoint 19.11
Left inverse of a morphism, vs. right inverse 3.10
Legitimate conglomerate 2.3
Legitimate quasicategory 6.16
Lifting of (E, M)-factorizations vs. E-monadic functor 20.24
Lifting of (E, M)-factorizations, uniquely 20.23
Lifting of (Extremal Epi, Mono-Source)-factorizations uniquely, vs. algebraic category 23.31
Lifting of an adjoint situation 21.26
Lifting of an adjoint situation vs. topological category 21.28
Lifting of colimits 13.17
Lifting of limits 13.17
Lifting of limits vs. amnesticity 13.21
Lifting of limits vs. create limits 13.20
Lifting of limits vs. detect limits 13.34
Lifting of limits vs. preserve small limits 13.19
Lifting of limits vs. reflect limits 13.23
Lifting of limits vs. transportability 13E
Lifting of limits, uniquely, and reflect limits, vs. create limits 13.25
Limit (of a diagram) 11.3 ff
Limit (of a diagram) construction via large colimits 12.7
Limit (of a diagram) creation 13.17
Limit (of a diagram) detection, = detection of limit 13.22
Limit (of a diagram) is extremal mono-source 11.6
Limit (of a diagram) vs. factorization 14.16
Limit (of a diagram) vs. hom-functors 13H
Limit (of a diagram) vs. initial object 11A
Limit (of a diagram) vs. intersection 11.25
Limit (of a diagram) vs. pullback square 11.9
Limit (of a diagram) vs. reflective subcategory 13.28
Limit (of a diagram), concrete, = concrete limit 13.12
Limit (of a diagram), inductive 11.28
Limit (of a diagram), inverse 11.4
Limit (of a diagram), lifting of 13.17 13D 13E
Limit (of a diagram), lifting of vs. topological functor 21.15
Limit (of a diagram), preservation of, = preservation of limit 13.1 ff 13B
Limit (of a diagram), preservation of, vs. preservation of monos 13.5
Limit (of a diagram), preservation of, vs. preservation of strong limits 13.1
Limit (of a diagram), preservation of, vs. topological functor 21.15
Limit (of a diagram), projective 11.4 11B
Limit (of a diagram), reflection of 13.22 13G 17.13
Limit (of a diagram), uniqueness 11.7
Limit-closed subcategory 13.26 13I 13J
Limit-closed subcategory vs. isomorphism-closed subcategory 13.27
Limit-dense subcategory, rarity 12E
Locally presentable category 20H
M-action, category of all M-actions and action homomorphisms 3.26
M-actions as functors from a monoid M to Set 3.20(13)
M-initially closed subcategory, vs. concretely E-reflective subcategory 22.9
M-reducible 28.13
M-sources, closed under the formation of 16.7
M-subobject, = singleton M-source 16.8
M-topological category 21.38 ff
M-topological category is E-reflective in some topological category 21.40
M-topological category vs. subcategory of a functor-structured category 22.9
M-topological category, characterization theorem 21.40
M-topological category, fibre-small, characterization 22.9
M-topological functor 21K
M-topological structure theorem 22.9
M-topos 28.7
| M-transformation 6.5
Mac Neille completion 21H
Mac Neille completion, vs. solid category 25G
Map, quotient, = quotient map 9.27
Matching condition see Object-free category
Maximal essential extension 9.20
Maximal essential extension vs. injective object 9F
Minimal injective extension 9.20
Minimal injective extension vs. smallest injective extension 9G
Modification, amnestic, = amnestic modification 5.6 5.33 5.34 5F
Modifications of structure, vs. (co)reflective subcategory 4.17 4.26
Monad 20.1 ff
Monad gives rise to an adjoint situation 20.7
Monad morphism 20.55
Monad on Set is finitary if and only if the associated construct is finitary 24.6
Monad on Set is regular 20.22
Monad, associated with an adjoint situation 20.3 20A
Monad, finitary 24.4
Monad, idempotent 20F
Monad, regular 20.21
Monad, trivial 20.2
Monad, with rank 20G
Monadic concrete category 20.8 ff
Monadic concrete category vs. (Epi, Mono-Source)-factorization 20.49
Monadic concrete category vs. adjoint functor 20.46
Monadic concrete category vs. co-wellpoweredness 20.29
Monadic concrete category vs. concrete functor 20E
Monadic concrete category vs. essentially algebraic category 23.16
Monadic concrete category vs. extremal co-wellpoweredness 20.48
Monadic concrete category vs. factorization structure 20.28
Monadic concrete category vs. final morphism 20.28
Monadic concrete category vs. finitary variety 24.7
Monadic concrete category vs. monadic subcategory 20.19
Monadic concrete category vs. reflective subcategory 20.18
Monadic concrete category vs. varietor 20.56 20.57 20.58
Monadic concrete category,  its associated category of algebras 20.40
Monadic concrete category, cocompleteness of 20D
Monadic concrete category, properties of 20.12
Monadic construct 20.34 ff
Monadic construct, bounded, vs. bounded variety 24.11
Monadic construct, characterization theorem for 20.35
Monadic construct, is complete, cocomplete, wellpowered, co-wellpowered, and has regular factorizations 20.34
Monadic construct, is regularly algebraic 23.37
Monadic construct, vs. algebraic construct 23.41
Monadic construct, vs. coequalizer of congruence relation 20.35
Monadic construct, vs. creation of finite limits 20.35
Monadic functor 20.8 ff
Monadic functor creates absolute colimits 20.16
Monadic functor need not detect colimits 20.47
Monadic functor need not reflect regular epimorphisms 20.52
Monadic functor regularly, = regularly monadic functor 20.21 ff
Monadic functor vs. colimit 20.13
Monadic functor vs. essentially algebraic functor 23C
Monadic functor vs. extremal monomorphism 20O
Monadic functor vs. order preserving map 20N
Monadic functor vs. preservation of extremal epimorphisms 20.50
Monadic functor vs. preservation of regular epimorphisms 20.50
Monadic functor vs. regularly monadic functor 20.32 20.35
Monadic functor vs. solid functor 25F
Monadic functor, characterization theorem for 20.17
Monadic functor, composition of, need not be monadic 20.45
Monadic functor, deficiencies of 20.45 ff
Monadic functor, properties of 20.12
Monadic subcategory, vs. monadic category 20.18
Monadic towers 20J
Mono-source 10.5 ff
Mono-source characterization 10A
Mono-source is extremal in balanced category 10.12
Mono-source is initial vs. essentially algebraic functor 23.2
Mono-source is initial vs. monadic category 20.12
Mono-source is initial vs. reflection of limits 17.13 17.14
Mono-source preservation implied by (Generating, —)-factorization for 2-sources 17.12
Mono-source preservation, by representable functors 10.7
Mono-source preserved by composition 10.9
Mono-source preserved by first factor 10.9
Mono-source reflection, by faithful functors 10.7
Mono-source vs. (E, M)-category 15.6—15.9
Mono-source vs. balanced category 10.12
Mono-source vs. initial source 17.13
Mono-source vs. monomorphism 10.26
Mono-source vs. point-separating source 10.8 10T
Mono-source vs. preservation of limits 13.5
Mono-source vs. pushout 11P
Mono-source vs. subsource 10.10
Mono-source, extremal, = extremal mono-source 10.11
Mono-transformation 6.5 7R
Monoid (as a category) 3.3(4)
Monomorphism 7.32 ff
Monomorphism as retraction means isomorphism 7.36
Monomorphism is pullback stable 11.18
Monomorphism preserved and reflected by equivalence functor 7.47
Monomorphism preserved by products 10.35
Monomorphism preserved by representable functor 7.37
Monomorphism vs. (E, M)-structured category 14.9
Monomorphism vs. coequalizer 7.70
Monomorphism vs. congruence relation 11.20 11R
Monomorphism vs. embedding 8.7
Monomorphism vs. free object 8.28 8.29
Monomorphism vs. mono-source 10.26
Monomorphism vs. preservation of limits 13.5
Monomorphism vs. pullback square 11.15 11.16
Monomorphism vs. regular monomorphism 7O
Monomorphism vs. section 7.35 7P
Monomorphism, closed under composition 7.34
Monomorphism, extremal, = extremal monomorphism 7.61 ff
Monomorphism, normal 7C
Monomorphism, reflected by faithful functor 7.37
Monomorphism, regular, = regular monomorphism 7.56 ff
Monomorphism, split, = section 7.19 ff
Monomorphism, strict, = strict monomorphism 7.76 7D
Monomorphism, types of 7.76
Monoreflective subcategory 16.1
Monoreflective subcategory, is bireflective 16.3
Monotopological category 21.38 ff
Monotopological construct vs. concrete products 21.42
Monotopological construct vs. initial subobjects 21.42
Monotopological construct, characterization of fibre-small 22.10
Monotopological constructvs. subconstruct of a functor-structured construct 22.10
Morphism 3.1 ff
Morphism class as corresponding object-free category 3.54
Morphism class of a category 3.2
Morphism class of small category is a set 3.45
Morphism in an object-free category 3.53
Morphism, (co)domain of 3.2
Morphism, coessential 9.27
Morphism, composite of see Composition of morphisms
Morphism, constant 7A 10W
Morphism, diagonal 10V 10W
Morphism, epi- see Epimorphism
Morphism, evaluation 27.2
Morphism, exponential 27.2
Morphism, final, = final morphism 8.10 ff
Morphism, initial, = initial morphism 8.6 ff
Morphism, isomorphism 3.8
Morphism, mono- see Monomorphism
Morphism, partial 28.1
Morphism, product of 10.34
Morphism, quotient, = quotient morphism 8.10
Morphism, retraction 7.24 ff
Morphism, section 7.19 ff
Morphism, zero 7A
Multiple equalizer 11.4
Multiple pullback 11L—11N 12C
Multiple pullback preservation 13A
n-th power functor 3.20(10)
n-tuple of sets or classes 2.1 2.2
Natural equivalence, = natural isomorphism 6.5
Natural isomorphism 6.5
Natural numbers 2.1
Natural sink 11.27
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