Timeline for Distributivity / commutativity of pushouts and pullbacks
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 3, 2011 at 5:53 | comment | added | Steve Lack | only just saw this - belated thanks and g'day | |
| Nov 19, 2010 at 6:56 | vote | accept | roger123 | ||
| Nov 19, 2010 at 1:28 | comment | added | Steve Lack | Yes, that's it. | |
| Nov 18, 2010 at 14:10 | comment | added | roger123 | Thank you for the answer, Steve. May I formulate it in this way: The commuting property is fulfilled iff for every functor $F:C\times D\to A$ it does not matter if I first apply the colimit functor to the first "factor" and get a functor $F':D\to A$ to which I apply the limit functor or if I do it the other way round? | |
| Nov 18, 2010 at 10:40 | comment | added | Steve Lack | Good point about the homotopy case. One example (in the non-homotopy case) where pushouts and pullbacks do commute is in a groupoid. But pullbacks and pushouts in groupoids are not very interesting. | |
| Nov 18, 2010 at 3:06 | comment | added | Tom Goodwillie | If we pass from category theory to homotopy theory, we can consider whether D-shaped homotopy limits commute (up to natural weak equivalence) with C-shaped homotopy colimits. This is not so rare. If the category is pointed then it is the same as what is commonly called stable. Typical examples are spectra, or (unbounded) chain complexes of R-modules. It's also the same as saying that a square diagram is a homotopy pushout iff it is a homotopy pullback. Also the same as: finite homotopy colimits commute with all homotopy limits (or vice versa). | |
| Nov 17, 2010 at 23:15 | comment | added | David Roberts♦ | Welcome, Steve! | |
| Nov 17, 2010 at 23:04 | history | answered | Steve Lack | CC BY-SA 2.5 |