| 11. | More precisely it can be defined as the set of homotopy classes
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| 12. | It inherits the idea of Serre that a covering preserves homotopy.
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| 13. | The morphisms are given by homotopy classes of edges between vertices.
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| 14. | Their paper also foreshadowed several later developments in homotopy type theory.
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| 15. | This has been very important in the study of homotopy groups.
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| 16. | Homotopy type theory continues in this line using type theory.
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| 17. | Thus, the differential equation solutions can be classified into homotopy classes.
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| 18. | There exists a homotopy theoretic analogue of the s-cobordism theorem.
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| 19. | Furthermore, every cone is contractible to the vertex point by the homotopy
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| 20. | One interpretation is in terms of these homotopy classes of chain maps.
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