Timeline for Why is the path fibration a strong Hurewicz fibration?
Current License: CC BY-SA 3.0
9 events
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| Jul 6, 2013 at 18:10 | comment | added | Andrej Bauer | Ok, thanks, I will have another look. Your comments are helpful. | |
| Jul 6, 2013 at 15:57 | history | edited | Karol Szumiło | CC BY-SA 3.0 |
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| Jul 6, 2013 at 15:54 | comment | added | Karol Szumiło | ... Thus the definitions coincide and Lemma 4.3 indeed proves that $X^I \to X \times X$ is a strong fibration in both senses. | |
| Jul 6, 2013 at 15:53 | comment | added | Karol Szumiło | Maybe this will clarify things. Actually, it's Cole's definition that is a priori stronger than May's and Sigurdsson's. For Cole a strong fibration is a map with RLP with respect to all acyclic cofibrations, for May and Sigurdsson it is one with RLP with respect to pushout products of arbitrary cofibrations with $\{ 0 \} \to I$. Cole proves that every such pushout product is an acyclic cofibration (Prop. 2.10) and that every acyclic cofibration is a retract of such a pushout product (Prop 2.13)... | |
| Jul 6, 2013 at 15:09 | comment | added | Karol Szumiło | I don't understand your remark. In the proof of Lemma 3.4 Cole starts with the case of an arbitrary acyclic cofibration ($g : Z \to W$ in his notation) and then reduces it to "a specific case which is easily related to the geometry of the interval". The reduction itself also heavily uses topology of the interval. | |
| Jul 6, 2013 at 13:32 | comment | added | Andrej Bauer | I am sorry but this does not seem very helpful. In my case the starting point is a general cofibration $i: A \to X$, whereas Lemma 3.4 in Cole considers a specific case which is easily related to the geometry of the interval. | |
| Jul 6, 2013 at 8:55 | history | edited | Karol Szumiło | CC BY-SA 3.0 |
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| Jul 6, 2013 at 8:42 | history | edited | Karol Szumiło | CC BY-SA 3.0 |
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| Jul 6, 2013 at 8:36 | history | answered | Karol Szumiło | CC BY-SA 3.0 |