Which is the model structure on $ \text{sSet} $ (category of simplicial sets) that makes $\text{sSet}$ Quillen equivalent to the category $ \text{Cat} $ (of small categories) by the adjunction realization $-|$ nerve?
Is it possible/reasonable to describe this model structure without using this adjunction?
Is there a reference you can give me about this kind of stuff?
Thank you in advance
If you can understand written French, I warmly invite you to read the introduction (i.e. pages 3 to 19) of this book to find your answer and much more material.
And in case you can't, this book is a good reason to try learning it!