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The long exact sequence of homotopy n-groups
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- Journal:
- Mathematical Structures in Computer Science / Volume 33 / Issue 8 / September 2023
- Published online by Cambridge University Press:
- 07 September 2023, pp. 679-687
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- Article
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Working in homotopy type theory, we introduce the notion of n-exactness for a short sequence
$F\to E\to B$ of pointed types and show that any fiber sequence 
$F\hookrightarrow E \twoheadrightarrow B$ of arbitrary types induces a short sequence
that is n-exact at
$\| E\|_{n-1}$. We explain how the indexing makes sense when interpreted in terms of n-groups, and we compare our definition to the existing definitions of an exact sequence of n-groups for 
$n=1,2$. As the main application, we obtain the long n-exact sequence of homotopy n-groups of a fiber sequence.
