ISSN:
1572-9095
Schlagwort(e):
Abelian category
;
category
;
directed set
;
directed system
;
factorization structure
;
inverse system
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract We present two related categorical constructions. Given a category C, we construct a category C[d], the category of directed systems in C. C embeds into C[d], and if C has enough colimits, then C is monadic over C[d]. Also, if E,M is a factorization structure for C, then C[d] has a related factorization structure Ed Md such that if E consists entirely of monic arrows, then so does Ed and the Ed-quotient poset of an object A is naturally the poset of directed downsets of the E-quotient poset of A. Similarly, if M consists entirely of monicarrows, then so does Md and the Md-subobject poset of an object A is naturally the poset of directed downsets of the M-subobject poset. C[d] has completeness and cocompleteness properties at least as good as those of C, and it is abelian if C is. Dualization gives the other construction: a category C[i], the category of inverse systems in C, into which C also embeds and which satisfies similar properties, except that directed downsets in the E-quotient and M-subobject posets are replaced by directed upsets.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1023/A:1008600332095
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