20:
1042:
973:
767:
339:
407:
681:. More precisely, given a substructure closed under some operations, the inclusion map will be an embedding for tautological reasons. For example, for some binary operation
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40:
707:
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555:
1139: – In mathematics, a function that always returns the same value that was used as its argument
560:
502:
457:
175:
1241:
802:
684:
772:
612:
181:
532:
374:) is sometimes used in place of the function arrow above to denote an inclusion map; thus:
8:
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96:
49:
1234:
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126:
72:
25:
1245:
1162:
1136:
1037:{\displaystyle \operatorname {Spec} \left(R/I^{2}\right)\to \operatorname {Spec} (R)}
899:
860:
789:
is consistently computed in the sub-structure and the large structure. The case of a
1069:
968:{\displaystyle \operatorname {Spec} \left(R/I\right)\to \operatorname {Spec} (R)}
864:
790:
1205:
1265:
910:
670:
1127:
883:
606:
In many instances, one can also construct a canonical inclusion into the
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1045:
891:
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19:
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805:
means such constants must already be given in the substructure.
1193:; every inclusion relation gives rise to an insertion function.
144:
90:
43:
178:
762:{\displaystyle \iota (x\star y)=\iota (x)\star \iota (y)}
334:{\displaystyle \iota :A\rightarrow B,\qquad \iota (x)=x.}
1161:. Providence, RI: AMS Chelsea Publishing. p. 5.
1130: – continuous mapping between topological spaces
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411:(However, some authors use this hooked arrow for any
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129:
99:
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1132:
Pages displaying wikidata descriptions as a fallback
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1111:
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967:
909:. Another example, more sophisticated, is that of
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34:
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1156:
898:in an older and unrelated terminology) such as
1198:
890:objects (which is to say, objects that have
343:An inclusion map may also referred to as an
402:{\displaystyle \iota :A\hookrightarrow B.}
1231:
905:to submanifolds, giving a mapping in the
1240:. New York, NY: Academic Press. p.
793:is similar; but one should also look at
18:
1264:
878:come in different kinds: for example
1173:Note that "insertion" is a function
13:
1157:MacLane, S.; Birkhoff, G. (1967).
14:
1288:
801:element. Here the point is that
677:; thus, such inclusion maps are
1236:Fundamental Concepts of Algebra
499:, if there is an inclusion map
309:
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1150:
1031:
1025:
1016:
962:
956:
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665:Applications of inclusion maps
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319:
313:
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1:
1143:
797:operations, which pick out a
576:{\displaystyle f\circ \iota }
524:{\displaystyle \iota :A\to X}
1272:Basic concepts in set theory
859:the inclusion map yields an
7:
1183:and "inclusion" a relation
1121:
913:, for which the inclusions
808:Inclusion maps are seen in
10:
1293:
834:strong deformation retract
669:Inclusion maps tend to be
372:RIGHTWARDS ARROW WITH HOOK
418:This and other analogous
262:treated as an element of
554:, then one can form the
199:that sends each element
697:{\displaystyle \star ,}
1277:Functions and mappings
1232:Chevalley, C. (1956).
1113:
1086:
1062:
1038:
969:
853:
826:
783:
782:{\displaystyle \star }
769:is simply to say that
763:
698:
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628:{\displaystyle R\to Y}
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577:
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191:{\displaystyle \iota }
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83:
63:
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16:Set-theoretic function
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827:
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426:are sometimes called
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894:; these are called
353:canonical injection
1213:Unicode Consortium
1206:"Arrows – Unicode"
1112:{\displaystyle R.}
1109:
1082:
1058:
1034:
965:
900:differential forms
874:Inclusion maps in
867:(that is, it is a
852:{\displaystyle X,}
849:
822:
810:algebraic topology
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759:
694:
655:{\displaystyle f.}
652:
625:
599:{\displaystyle f.}
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521:
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446:
428:natural injections
399:
358:A "hooked arrow" (
345:inclusion function
331:
278:{\displaystyle B:}
275:
255:{\displaystyle x,}
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209:
188:
163:{\displaystyle B,}
160:
133:
117:
109:{\displaystyle A.}
106:
79:
62:{\displaystyle B,}
59:
32:
1137:Identity function
1085:{\displaystyle I}
1061:{\displaystyle R}
1044:may be different
825:{\displaystyle A}
547:{\displaystyle X}
492:{\displaystyle Y}
472:{\displaystyle X}
449:{\displaystyle f}
232:{\displaystyle A}
212:{\displaystyle x}
136:{\displaystyle A}
82:{\displaystyle B}
35:{\displaystyle A}
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1110:
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1070:commutative ring
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907:other direction
865:homotopy groups
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791:unary operation
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933:
929:
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922:
911:affine schemes
848:
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78:
58:
55:
31:
15:
9:
6:
4:
3:
2:
1289:
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1269:
1267:
1253:
1251:0-12-172050-0
1247:
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1238:
1237:
1228:
1214:
1207:
1201:
1194:
1191:
1187:
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1177:
1170:
1168:0-8218-1646-2
1164:
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1135:
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904:
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893:
889:
888:Contravariant
885:
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862:
846:
843:
835:
819:
811:
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732:
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723:
720:
717:
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691:
688:
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676:
672:
671:homomorphisms
662:
649:
646:
638:
635:known as the
622:
616:
609:
593:
590:
570:
567:
564:
557:
541:
534:
518:
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506:
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436:
431:
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425:
424:substructures
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363:
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185:
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173:
172:inclusion map
157:
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146:
130:
122:
103:
100:
92:
76:
56:
53:
45:
29:
21:
1235:
1227:
1216:. Retrieved
1200:
1189:
1185:
1179:
1175:
1172:
1158:
1152:
906:
902:
884:submanifolds
873:
863:between all
807:
798:
668:
432:
427:
417:
410:
357:
352:
348:
344:
342:
171:
118:
1128:Cofibration
861:isomorphism
556:restriction
121:mathematics
1266:Categories
1218:2017-02-07
1144:References
880:embeddings
679:embeddings
433:Given any
1046:morphisms
1023:
1017:→
986:
954:
948:→
924:
896:covariant
892:pullbacks
812:where if
777:⋆
748:ι
745:⋆
733:ι
721:⋆
712:ι
689:⋆
620:→
571:ι
568:∘
531:into the
516:→
507:ι
420:injective
413:embedding
391:↪
382:ι
349:insertion
311:ι
301:→
292:ι
186:ι
170:then the
1122:See also
1048:, where
903:restrict
876:geometry
799:constant
608:codomain
456:between
435:morphism
369:↪
176:function
91:superset
1159:Algebra
803:closure
795:nullary
458:objects
351:, or a
174:is the
1248:
1165:
1092:is an
533:domain
366:
145:subset
44:subset
1209:(PDF)
1094:ideal
1068:is a
832:is a
637:range
347:, an
143:is a
123:, if
89:is a
42:is a
1246:ISBN
1163:ISBN
1072:and
1020:Spec
983:Spec
975:and
951:Spec
921:Spec
479:and
364:21AA
69:and
1096:of
882:of
871:).
836:of
673:of
639:of
583:of
415:.)
239:to
219:of
147:of
119:In
93:of
46:of
1268::
1244:.
1211:.
1188:⊂
1178:→
1171:.
886:.
430:.
362:U+
355:.
1254:.
1242:1
1221:.
1190:U
1186:S
1180:U
1176:S
1107:.
1104:R
1080:I
1056:R
1032:)
1029:R
1026:(
1013:)
1007:2
1003:I
998:/
994:R
990:(
963:)
960:R
957:(
944:)
940:I
936:/
932:R
928:(
847:,
844:X
820:A
757:)
754:y
751:(
742:)
739:x
736:(
730:=
727:)
724:y
718:x
715:(
692:,
650:.
647:f
623:Y
617:R
594:.
591:f
565:f
542:X
519:X
513:A
510::
487:Y
467:X
444:f
397:.
394:B
388:A
385::
329:.
326:x
323:=
320:)
317:x
314:(
307:,
304:B
298:A
295::
273::
270:B
250:,
247:x
227:A
207:x
158:,
155:B
131:A
104:.
101:A
77:B
57:,
54:B
30:A
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