Definition talk:Projective Module

The definition
This is not the usual definition of projective module. It does not work in abelian categories. The definition should be: projective object in a category of modules.


 * One of the problems we have on is people bringing their own understanding of what things are and what things mean without any reference to published sources, which means it is not possible to corroborate those definitions. When you then get more than one contributor bringing completely different definitions hanging off the same name, there is bound to be a conflict.


 * I can see that is what is going on here.


 * Please, if you wish to contribute to this area, it is requested that you reference every definition to which you contribute against the hard-copy source (or an instance of the small set of accepted internet resources which you will find listed in the Help pages), preferably in the standard format.


 * It is appreciated that this is something of a burden to the casual contributor, but the mathematics here is sufficiently new and abstruse that there are possibly multiple definitions and understandings of numerous concepts. As you can see by investigating the structure of, multiply-defined concepts (specifically, non-equivalent definitions) are typically handled by an "also defined as" section, where the differences between the concepts are brought to light, and (if necessary) a page explaining the differences, and whatever consequences of those differences are. --prime mover (talk) 07:05, 24 July 2021 (UTC)


 * Thank you very much for your feedback. I will provide references for the definitions I write.


 * For example here: : $\S \text 2.2$, the 'standard' definition of projective module I mentioned is given. I would like to change the definition given in the article and turn the old definition into a theorem. I think this is okay, since the only old articles that link to Definition:Projective Module are just definitions. All of this is not really a conflict, since whenever projective modules are defined all definitions are equivalent. It's just a matter of style and generality since in an arbitrary abelian category there is no definition of free object. One can make this precise, as explained here. --Wandynsky (talk) 12:57, 24 July 2021 (UTC)