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Tim Campion
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Lurie uses A.2.6.7 to prove the "easy" direction of Jeff Smith's theorem in A.2.6.8, namely that every combinatorial model category arises from the construction of the theorem. This part of the theorem is proven in the last sentence of the current revision on the nlab page ("To prove the converse,..."), where the facts of A.2.6.7 are indeed referred to, but they are regarded as being well-known. This seems reasonable to me because A.2.6.7 is a general fact about accessible categories, in no way specialized to the study of model categories. But it never hurts to be more explicit; one should always feel free to add details to an nlab page.

Lurie uses A.2.6.7 to prove the "easy" direction of Jeff Smith's theorem in A.2.6.8, namely that every combinatorial model category arises from the construction of the theorem. This part of the theorem is proven in the last sentence of the current revision on the nlab page ("To prove the converse,..."), where the facts of A.2.6.7 are indeed referred to, but they are regarded as being well-known. This seems reasonable to me because A.2.6.7 is a general fact about accessible categories, in no way specialized to the study of model categories.

Lurie uses A.2.6.7 to prove the "easy" direction of Jeff Smith's theorem in A.2.6.8, namely that every combinatorial model category arises from the construction of the theorem. This part of the theorem is proven in the last sentence of the current revision on the nlab page ("To prove the converse,..."), where the facts of A.2.6.7 are indeed referred to, but they are regarded as being well-known. This seems reasonable to me because A.2.6.7 is a general fact about accessible categories, in no way specialized to the study of model categories. But it never hurts to be more explicit; one should always feel free to add details to an nlab page.

Source Link
Tim Campion
  • 64k
  • 13
  • 143
  • 384

Lurie uses A.2.6.7 to prove the "easy" direction of Jeff Smith's theorem in A.2.6.8, namely that every combinatorial model category arises from the construction of the theorem. This part of the theorem is proven in the last sentence of the current revision on the nlab page ("To prove the converse,..."), where the facts of A.2.6.7 are indeed referred to, but they are regarded as being well-known. This seems reasonable to me because A.2.6.7 is a general fact about accessible categories, in no way specialized to the study of model categories.