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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJun 14th 2018
• (edited Jun 14th 2018)

gave this statement its own entry, as it is being referenced or used in a variety of other entries. Also spelled out a proof. Not a short one but, hopefully, a conceptual one.

• CommentRowNumber2.
• CommentAuthorDylan Wilson
• CommentTimeJun 14th 2018

Maybe a quicker proof: By Quillen’s theorem A, you need to show that $C_{/(x,y)}$ is contractible; but it has a final object! So you’re done.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeJun 14th 2018

Feel invited to add other proofs to the entry!