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• CommentRowNumber1.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 1st 2020

Created.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 2nd 2020

I have fixed the broken intended hyperlinks and added hyperlinks to a bunch of further keywords. Added TOC, floating topic context and plural redirect.

Finally, bring pedantic, I changed the lead-in from

A premodel category is a relaxation of the notion of a model category.

to

The notion of a premodel category is a relaxation of the notion of a model category.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 2nd 2020

Also slightly edited this sentence, for readability (I hope):

Model categories can be singled out among premodel categories by imposing the additional requirement that the class

$W \coloneqq AF \circ AC$

obtained by composing elements of $AC$ with those of $AF$, is closed under the 2-out-of-3 property.

• CommentRowNumber4.
• CommentAuthorHurkyl
• CommentTimeMay 8th 2020

Mention the distinction between anodyne and trivial cofibrations

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMay 8th 2020

I have equipped the mentioning of the terminology “anodyne (co)fibration” with a pointer to anodyne morphism

• CommentRowNumber6.
• CommentAuthorHurkyl
• CommentTimeMay 9th 2020

Added related concepts: model category and weak model category.