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http://hdl.handle.net/2080/211
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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
http://www.math.sinica.edu.tw/bulletin/d331/33102.pdf |
| URI: | http://hdl.handle.net/2080/211 |
| Appears in Collections: | Journal Articles
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