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Finite preorders and topological descent II: étale descent

✍ Scribed by George Janelidze; Manuela Sobral

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
92 KB
Volume
174
Category
Article
ISSN
0022-4049

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✦ Synopsis

It is known that every e ective (global-) descent morphism of topological spaces is an e ective à etale-descent morphism. On the other hand, in the predecessor of this paper we gave examples of:

• a descent morphism that is not an e ective à etale-descent morphism;

• an e ective à etale-descent morphism that is not a descent morphism.

Both of the examples in fact involved only ÿnite topological spaces, i.e. just ÿnite preorders, and now we characterize the e ective à etale-descent morphisms of preorders=ÿnite topological spaces completely.

📜 SIMILAR VOLUMES

Finite preorders and Topological descent
Finite preorders and Topological descent I
✍ George Janelidze; Manuela Sobral 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 178 KB

It is shown that the descent constructions of ÿnite preorders provide a simple motivation for those of topological spaces, and new counter-examples to open problems in Topological descent theory are constructed.