2008Homology Homotopy and ApplicationsOpen access

On the homotopy theory of $n$-types

Georg Biedermann

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Abstract

We achieve a classification of n-types of simplicial presheaves in terms of (n -1)-types of presheaves of simplicial groupoids.This can be viewed as a description of the homotopy theory of higher stacks.As a special case we obtain a good homotopy theory of (weak) higher groupoids.

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We achieve a classification of n-types of simplicial presheaves in terms of (n -1)-types of presheaves of simplicial groupoids.This can be viewed as a description of the homotopy theory of higher stacks.As a special case we obtain a good homotopy theory of (weak) higher groupoids.

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We achieve a classification of n-types of simplicial presheaves in terms of (n -1)-types of presheaves of simplicial groupoids.This can be viewed as a description of the homotopy theory of higher stacks.As a special case we obtain a good homotopy theory of (weak) higher groupoids.

Key concepts: Homotopy, Mathematics, Cofibration, n-connected, Regular homotopy, Pure mathematics

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