What is a homotopy theory ?

https://prezi.com/m/vvvdcth44xms/the-unicity-of-the-homotopy-theory-of-higher-categories-notre-dame/

Some possibilities :

– a Quillen model category

– a homotopical category ( Dwyer-Kan-Smith)

– a category with any class of weak equivalences (a relative category is a category with a class of weak equivalences containing the identities )

https://meditationesdeprimaphilosophia.wordpress.com/category/homotopical-categories/

https://ncatlab.org/nlab/show/homotopical+category

https://ncatlab.org/nlab/show/model+category

https://ncatlab.org/nlab/show/relative+category

https://arxiv.org/abs/1011.1691

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