Page 123 - Textos de Matemática Vol. 45

Index
S-protomodular category, 98 C′ -unital category, 8
accessible Schreier split extension, 71
Baer sums in monoids, 89 Baer sums in semirings, 95
cartesian morphism, 103 centralizer of reflexive relations, 54 change-of-base functor, 23 commutative object, 7
connector, 44
conservative functor, 23 cooperating morphisms, 6 cooperator, 6
direction, 84
direction functor, 86
double centralizing relation, 47
faithful Schreier split extension, 71 fiber, 103
fibration, 103
fibration of homogeneous points, 23 fibration of points, 8
fibration of Schreier points, 23
homogeneous internal category, 36 homogeneous internal groupoid, 38 homogeneous reflexive graph, 29 homogeneous split epimorphism, 11 homogeneous split extension classi-
internal category, 35 internal group, 109 internal groupoid, 38 internal monoid, 107 internal reflexive graph, 29
jointly strongly epimorphic morphisms, 6
kernel equivalence relation, 5 kernel functor, 26
Mal’tsev category, 9 protomodular category, 97 reflexive relation, 29
Schreier equivalence relation, 29 Schreier internal category, 36 Schreier internal groupoid, 38 Schreier reflexive graph, 29 Schreier split epimorphism, 11 Schreier split extension classifier, 49 Schreier split short five lemma, 22 semidirect product of monoids, 52 semidirect product of semirings, 77 semiring, 57
shift functor, 110
simplicial notation, 104
simplicial ob ject, 104
special homogeneous surjection, 79 special Schreier extension, 81 special Schreier short five lemma,
fier, 52
81
115