# Batanin higher groupoids and homotopy types

@article{Cisinski2006BataninHG, title={Batanin higher groupoids and homotopy types}, author={Denis-Charles Cisinski}, journal={arXiv: Algebraic Topology}, year={2006} }

We prove that any homotopy type can be recovered canonically from its associated weak omega-groupoid. This implies that the homotopy category of CW-complexes can be embedded in the homotopy category of Batanin's weak higher groupoids.

## 26 Citations

### Homotopy theory of higher categories

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### Lectures on N-Categories and Cohomology

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### Adding inverses to diagrams II: Invertible homotopy theories are spaces

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In previous work, we showed that there are appropriate model category structures on the category of simplicial categories and on the category of Segal precategories, and that they are Quillen…

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### A Prehistory of n-Categorical Physics

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### Homotopy type theory and Voevodsky's univalent foundations

- MathematicsArXiv
- 2012

This paper serves as an introduction to both the general ideas of homotopy type theory as well as to some of the concrete details of Voevodsky's work using the well-known proof assistant Coq.

### Erratum to “Adding inverses to diagrams encoding algebraic structures” and “Adding inverses to diagrams II: Invertible homotopy theories are spaces”

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In previous work, we showed that there are appropriate model category structures on the category of simplicial categories and on the category of Segal precategories, and that they are Quillen…

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