Talk:Concrete category: Difference between revisions

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Mathematics B‑class Mid‑priority

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I have given this article a major overhaul. Previously, it contained one major factual inaccuracy (the assertion that Rel can not be concretized), unprofessional language ("roughly speaking", "in everyday life"), and failed to address several key issues such as the overlap between "abstract" and "concrete". I will expand section 5 after I have found some more references. Boy Waffle (talk) 18:44, 22 February 2008 (UTC)[reply]

I have made the promised addition, and a bit more. I have also taken the liberty of incrementing both the class and priority of this article. Boy Waffle (talk) 18:34, 26 February 2008 (UTC)[reply]

Rosicky uses a slightly stronger definition of concrete category in order to prove that every concrete category is isomorphic to (not merely equivalent to) a full subcategory of some category of models. It is clear, however, that every concrete category (in the larger sense) is equivalent to one of his; hence, I did not feel it necessary to discuss this issue in the article itself. Also, Freyd uses the word concrete to mean concretizable. Freyd's main theorem is stated in terms of based spaces; but he later notes that basepoints are not essential. Boy Waffle (talk) 18:34, 26 February 2008 (UTC)[reply]

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 {{maths rating
 |field = foundations
-|importance = low
+|importance = mid
-|class = start
+|class = B
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 I have given this article a major overhaul.  Previously, it contained one major factual inaccuracy (the assertion that '''Rel''' can not be concretized), unprofessional language ("roughly speaking", "in everyday life"), and failed to address several key issues such as the overlap between "abstract" and "concrete".  I will expand section 5 after I have found some more references. [[User:Boy Waffle|Boy Waffle]] ([[User talk:Boy Waffle|talk]]) 18:44, 22 February 2008 (UTC)
+: I have made the promised addition, and a bit more.  I have also taken the liberty of incrementing both the class and priority of this article.  [[User:Boy Waffle|Boy Waffle]] ([[User talk:Boy Waffle|talk]]) 18:34, 26 February 2008 (UTC)
+Rosicky uses a slightly stronger definition of concrete category in order to prove that every concrete category is ''isomorphic to'' (not merely ''equivalent to'') a full subcategory of some category of models.  It is clear, however, that every concrete category (in the larger sense) is equivalent to one of his; hence, I did not feel it necessary to discuss this issue in the article itself.  Also, Freyd uses the word ''concrete'' to mean ''concretizable''.  Freyd's main theorem is stated in terms of based spaces; but he later notes that basepoints are not essential. [[User:Boy Waffle|Boy Waffle]] ([[User talk:Boy Waffle|talk]]) 18:34, 26 February 2008 (UTC)