Timeline for Axiom of Replacement in Category Theory
Current License: CC BY-SA 2.5
3 events
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| Oct 6, 2010 at 2:17 | comment | added | Peter LeFanu Lumsdaine | I find that interesting too, but I don't think it proves much one way or the other. In previous periods, people implicitly assumed things like unrestricted comprehension (as shown to be inconsistent, by Russell), and continuity of all functions (not quite inconsistent, as things like SDG show, but certainly at odds with other more basic intuitions like the excluded middle). The things we implicitly use, and completely natural, often turn out to be just the standard assumptions of the culture we were educated in, not necessarily any more than that… | |
| Oct 6, 2010 at 1:15 | comment | added | arsmath | You could do it, but I find it interesting that in practice people just act as if replacement is true. Honestly, I personally had no idea that I was implicitly relying on replacement when thinking about categorical constructions, since at first glance it really does sound like a technical axiom you would never use. I feel like Moliere's Monsieur Jourdain discovering he's been speaking in prose his whole life. | |
| Oct 5, 2010 at 20:50 | history | answered | Martin Brandenburg | CC BY-SA 2.5 |