Topologized objects in categories and the Sullivan profinite completion

Deleanu, Aristide

doi:10.1016/0022-4049(82)90092-5

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Cited by 4 publications

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“…Some of the definitions below are chosen after [10]. For any category C and an object X of C a topologized object over X is a factorization…”

Section: Definitionmentioning

confidence: 99%

Homotopical localizations at a space

Przeździecki

2002

Topology and its Applications

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“…Some of the definitions below are chosen after [10]. For any category C and an object X of C a topologized object over X is a factorization…”

Section: Definitionmentioning

confidence: 99%

Homotopical localizations at a space

Przeździecki

2002

Topology and its Applications

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“…We can also use /?-finite or, for finite rings R, Ä-finite, spaces here. In this sense we have just answered Adams's questions (see also [9]) about an idempotent completion for topologized objects.…”

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confidence: 99%

“…Later, developing the "genetics of homotopy theory", Sullivan [24] remarked that a simple rigid completion functor could prove useful. A. Deleanu [9] defined the Sullivan completion on the topologized homotopy category, but left the question of idempotency open.…”

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confidence: 99%

An Idempotent Completion Functor in Homotopy Theory

Hastings¹

1985

Transactions of the American Mathematical Society

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Abstract.We observe that Artin-Mazur style R-completions (R is a commutative ring with identity) induce analogous idempotent completions on the weak prohomotopy category pro-Ho(Top). Because Ho(Top) is a subcategory of pro-Ho(Top) and pro-Ho(Top) is closely related to the topologized homotopy category of J. F. Adams and D. Sullivan, our construction represents the Sullivan completions as homotopy limits of idempotent functors. In addition, we show that the Sullivan completion is idempotent on those spaces (in analogy with the Bousfield and Kan R^-completion on /?-good spaces) for which its cohomology with coefficients in R agrees with that of our Artin-Mazur style completion. Finally, we rigidify the Artin-Mazur completion to obtain an idempotent Artin-Mazur completion on a category of generalized prospaces which preserves fibration and suitably defined cofibration sequences. (Our previous results on idempotency and factorization lift to the rigid completion.) Our results answer questions of Adams, Sullivan, and, later, A. Deleanu.

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Compact homotopy functors and the equivariant Sullivan profinite completion

Deleanu

1989

Journal of Pure and Applied Algebra

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Topologized objects in categories and the Sullivan profinite completion

Cited by 4 publications

References 2 publications

Homotopical localizations at a space

Homotopical localizations at a space

An Idempotent Completion Functor in Homotopy Theory

Compact homotopy functors and the equivariant Sullivan profinite completion

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