2005 / March Volume 32 No.1
Homotopy theory in groupoid enriched categories
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2005 / March
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Title | Homotopy theory in groupoid enriched categories |
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Pagination | 21-53 |
Abstract | The concepts of $h$-limits, strong $h$-limits (and their duals) and partial proofs of homotopy limit reduction theorems 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 homotopy 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 admits 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.
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AMS Subject Classification |
18D20
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Received |
2003-01-13
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