Timeline for Pushouts and products in categories
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 11, 2020 at 22:35 | history | became hot network question | |||
| Sep 11, 2020 at 22:04 | vote | accept | Jeff Strom | ||
| Sep 11, 2020 at 16:46 | answer | added | Mike Shulman | timeline score: 8 | |
| Sep 11, 2020 at 15:01 | comment | added | Simon Henry | Using this preservation of the pushout involved by products, you can expand $D \times Z$ as the colimit of some diagram with the shape of $3 \times 3$ array whose node are each products of the form $C \times Y, A \times Y, A \times X, \dots...$. You can then do some formal manipulation on the diagram to regroup the terms in the pushout and write the resulting colimits as this pushout of pushout... Let me know if you need more details. | |
| Sep 11, 2020 at 14:59 | comment | added | Simon Henry | The simplest standard assumption for this to work is that the two pushouts you assume at the begining should be preserved by products (at least by products by all the object appearing in the question). So this for example holds in any cartesian closed category (as in this case, product are left adjoint functors and hence preserve all colimits). I'm affraid writting a complete proof involves a bit to much diagrams for MO. The rough idea is as follows: | |
| Sep 11, 2020 at 14:35 | history | asked | Jeff Strom | CC BY-SA 4.0 |