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Mal'cev categories and fibration of pointed objects

✍ Scribed by Dominique Bourn


Publisher
Springer
Year
1996
Tongue
English
Weight
891 KB
Volume
4
Category
Article
ISSN
0927-2852

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We describe a su cient condition on a ΓΏnitely complete and cocomplete lextensive category X, under which the categorical smash product provides a canonical (symmetric, distributive with respect to ΓΏnite coproducts) monoidal structure on the category (1 ↓ X) of its pointed objects. We also show that

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Let F ΞΉ β†’ E f B be a fibration, we focus on the relation between the homotopy invariants cat E, cat F and cat B. The general formula due to Hardie says that cat E (cat ΞΉ + 1) β€’ (cat f + 1) -1; if the fibration is trivial, this upper bound can be replaced by cat F + cat B. In this paper, we introduce