A higher dimensional homotopy sequence (Q1605627)
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scientific article; zbMATH DE number 1770064
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A higher dimensional homotopy sequence |
scientific article; zbMATH DE number 1770064 |
Statements
A higher dimensional homotopy sequence (English)
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25 July 2002
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Given a continuous map \(f : X \to Y\) of pointed spaces, there is a well known long exact sequence relating the homotopy groups of \(X\), \(Y\) and \(Kf\), the homotopy kernel of \(f\). This note shows that this is in fact the projection of a `2-exact' (in a suitable sense) sequence of some homotopy pointed groupoids. The paper not only develops the machinery for this 2-exact sequence, but explores various aspects of a strong form of this notion of 2-exactness.
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homotopical algebra
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homotopy groupoids
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