1974
DOI: 10.1016/0022-4049(74)90010-3
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Existence of the Adams completion for CW-complexes

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Cited by 6 publications
(3 citation statements)
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“…Since the category CW as stated above is neither cocomplete nor small, Theorem 1.1 can not be used to show the existence of Adams completion of an object in the category CW with respect to the set of morphisms S n . However, we have the following result (Theorem 2.4) which is essentially Theorem 4.7 [2] and Theorem 3.8 [1] (it is also a generalization of the Theorem in [5] ).…”
Section: Proposition For a Given Object X Of The Category Cw There Ementioning
confidence: 99%
“…Since the category CW as stated above is neither cocomplete nor small, Theorem 1.1 can not be used to show the existence of Adams completion of an object in the category CW with respect to the set of morphisms S n . However, we have the following result (Theorem 2.4) which is essentially Theorem 4.7 [2] and Theorem 3.8 [1] (it is also a generalization of the Theorem in [5] ).…”
Section: Proposition For a Given Object X Of The Category Cw There Ementioning
confidence: 99%
“…In order to be able to use Brown's representability theorem ( [5], p. 157), one would like to have that the category of fractions should also belong to the same initial universe. Deleanu, in his papers [1,2] has assumed a certain condition (e.g., condition (*) in [1]), which precisely has the role of guaranteeing that the category of fractions remains within the given initial universe. In this note, we show that if the set of morphisms S is 'good' enough, then ^[S _1 ] is a small ^-category or, equivalently that condition (*) of Deleanu is satisfied.…”
Section: $Etsmentioning
confidence: 99%
“…REMARK 1. Now recall the following condition (*) of Deleanu [1,2]: For a given object Y of <#, there exists a subset T Y of the set S Y = {s:Y-> Y', s e S, V any object of ^} such that (i) T Y is an element of °U and (ii) for each s : Y-> Y' in S, there is a morphism s f eT Y and a morphism u of ^ such that us = s'; thus, there is a commutative diagram.…”
Section: And S Y Y > = Snmentioning
confidence: 99%