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Title: Homotopy Theory in Groupoid Enriched Categories
Authors: Behera, A
Keywords: Brown Complement Theorem
homotopy theory
Issue Date: 2005
Publisher: Institute of Mathematics, Academia Sinica
Citation: Bulletin of Institute of Mathematics, Academia Sinica, Vol 33, Iss 1 P 21-53
Abstract: The concepts of h-limits, strong h-limits (and their duals) and partial proofs of homotopy limit reduction the- orems relating to h-limits and strong h-limits are already known for a groupoid enriched category (g.e. category). In this paper the concepts of weak h-limits, quasi-limits (and their duals) are introduced in a g.e. category and the fuller version of the homo- topy limit reduction theorems concerning the four types of limits, i.e., weak h-limits, h-limits, strong h-limits and quasi-limits are proved. The previously called Brown Complement Theorem is proved under the restricted assumption that the g.e. category ad- mits only weak h-limits instead of h-limits and the generalized version of the Brown Complement Theorem is also proved which is relevant to the problem of showing under suitable smallness conditions that if a g.e. category admits all h-limits then it also admits all h-colomits.
Description: Copyright belongs to Institute of Mathematics, Academia Sinica
Appears in Collections:Journal Articles

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