Timeline for Is the box product of morphisms associative?
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 25, 2010 at 6:30 | comment | added | Harry Gindi | @Todd: Thanks! I was busy writing up my answer below, since I figured out a neat way to think about pushout problems like this in general. | |
| Oct 25, 2010 at 5:16 | comment | added | Todd Trimble | Even after you accepted, I rewrote the argument again to make it clearer. | |
| Oct 25, 2010 at 5:15 | history | edited | Todd Trimble | CC BY-SA 2.5 |
Rewrote to clarify the argument
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| Oct 25, 2010 at 5:10 | vote | accept | Harry Gindi | ||
| Oct 25, 2010 at 4:54 | comment | added | Todd Trimble | Harry, you're right: I gave you the wrong wide pushout! I rewrote my answer and I believe I got it right this time. | |
| Oct 25, 2010 at 4:53 | history | edited | Todd Trimble | CC BY-SA 2.5 |
corrected the diagram
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| Oct 25, 2010 at 3:57 | comment | added | Harry Gindi | @Todd: Here's the trouble: The wide pushout you gave me is just the cocartesian cube. In particular, the object we want to push out at the end is as follows: Let $$(AB)=A_1\otimes B_2\coprod_{A_1\otimes B_1} A_2\otimes B_1.$$ Then the object we want is: $$A_2\otimes B_2\otimes C_1 \coprod_{(AB)\otimes C_1} (AB)\otimes C_2.$$ And we would like to show that it is isomorphic to: $$A_1\otimes B_2\otimes C_2 \coprod_{A_1\otimes (BC)} A_2\otimes (BC).$$ How does the wide pushout help at all? | |
| Oct 25, 2010 at 3:11 | vote | accept | Harry Gindi | ||
| Oct 25, 2010 at 3:57 | |||||
| Oct 25, 2010 at 0:41 | comment | added | Harry Gindi | @Todd: The trouble I'm having is showing that it is either one of those wide pushouts! | |
| Oct 25, 2010 at 0:38 | vote | accept | Harry Gindi | ||
| Oct 25, 2010 at 0:41 | |||||
| Oct 25, 2010 at 0:32 | history | answered | Todd Trimble | CC BY-SA 2.5 |