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• CommentRowNumber1.
• CommentAuthorzskoda
• CommentTimeDec 2nd 2009

I created homotopy extension property and homotopy lifting property. If somebody wonders why I made identical copy of one of them on my personal nlab part is because there I want to keep conservative page for students and here in the main nlab I expect more vigorous extensions by others. On the other hand, I would like to have under homotopy lifting property mention of various variants like "soft map" homotopy lifting property, the homotopical variant of Dold etc. all in one place.

1. it seems the space Z becomes Y in the diagrams
• CommentRowNumber3.
• CommentAuthorzskoda
• CommentTimeDec 3rd 2009

The entry was incomplete yesterday, I had to leave before finishing. I will brush it up today and finish the proof of the proposition. Thanks for the tip.

• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeDec 3rd 2009
• (edited Dec 3rd 2009)

Added entries Strøm's theorem and weakly Hausdorff space. More references at Voevodsky motive.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMar 30th 2016

I gave homotopy extension property an Idea-section that starts with the transparent definition in terms of right homotopy.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeSep 15th 2021
• (edited Sep 15th 2021)

Have tried to polish up wording and typesetting of the Idea- and the Definition section. In particular, I have

• rendered the big diagram with TikZ;

• added missing remarks on cartesian closure for the reformulation in terms of right homotopies.

• added a reference pointer to

as well as to Hatcher’s book.

But it would be nice to give something closer to original references.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeSep 15th 2021

for the terminology “h-cofibration”

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeSep 15th 2021
• (edited Sep 15th 2021)

hm, now I see that “h-cofibration” redirects to here but has never been mentioned here, while it has been and is mentioned at Hurewicz cofibration.

Am moving the redirect to there…

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