Timeline for Who introduced direct limits?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 21, 2020 at 22:10 | comment | added | Robert Furber | @PaulTaylor I believe Pontryagin concerned himself with filtered colimits because they give a way of calculating the dual group to a cofiltered limit. At least, that is my reading of the bottom of p. 197 of the article suggested by Cameron Zwarich. I can't be certain because both my German and my understanding of the historical terminology of group theory and algebraic topology are not up to scratch. | |
| Apr 21, 2020 at 17:58 | comment | added | Paul Taylor | @RobertFurber Yes, I believe you are correct. I was misled by the reference to groups, where profinite Galois groups are natural and I wonder why one would draw attention to filtered colimits. | |
| Apr 21, 2020 at 17:24 | comment | added | Robert Furber | @PaulTaylor "Direct limit" is the old-fashioned name for a filtered colimit (indexed by a poset), rather than a cofiltered limit, which were called an "inverse limit", or "projective limit". | |
| Apr 21, 2020 at 15:51 | comment | added | Paul Taylor | That what categorists would now call cofiltered limits were first introduced for groups in the 1930s is entirely plausible. The unification of this notion with products, equalisers and pullbacks in category theory was made by Peter Freyd in his thesis in about 1963. | |
| Apr 20, 2020 at 20:50 | comment | added | Robert Furber | I think an early example outside groups was Dieudonné and Schwartz's paper on (LF) spaces. Each time it occurs, «limite inductive» is put in (French) quotation marks, as if the term is being used slightly outside its strict meaning. Schwartz's earlier papers describe the topology on compactly supported test functions directly in terms of convergence, rather than as the direct limit of a sequence of Fréchet spaces. | |
| Apr 20, 2020 at 19:43 | comment | added | YCor | It's hard to say when it was first done: it might have been done first in significant particular case, etc. Then maybe formalized but not in a very definite way. Also category theory unified the notion with the dual notions since it allows to treat arrows and their opposite in the same point of view. And of course the categorical definition doesn't supersede any specific case: how some kind of limits can be described in a given category of algebraic structures is also part of the job. | |
| Apr 20, 2020 at 19:28 | history | edited | YCor |
edited tags
|
|
| S Apr 20, 2020 at 19:18 | history | suggested | Jeppe Stig Nielsen | CC BY-SA 4.0 |
linkify MR reference
|
| Apr 20, 2020 at 18:31 | review | Suggested edits | |||
| S Apr 20, 2020 at 19:18 | |||||
| Apr 19, 2020 at 20:51 | history | became hot network question | |||
| Apr 19, 2020 at 18:17 | answer | added | Cameron Zwarich | timeline score: 28 | |
| Apr 19, 2020 at 17:02 | answer | added | Andrés E. Caicedo | timeline score: 23 | |
| Apr 19, 2020 at 13:17 | comment | added | Gerald Edgar | Probably it was done first with groups? At first just a sequence of groups. | |
| Apr 19, 2020 at 12:57 | history | edited | Monroe Eskew | CC BY-SA 4.0 |
deleted 4 characters in body
|
| Apr 19, 2020 at 12:45 | history | asked | Monroe Eskew | CC BY-SA 4.0 |