Talk:Glossary of category theory

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I started this article, as there are many terms in category theory and the glossary article can come handy like many others. I know there are a good deal of overlaps right now but I think we can keep each main article (e.g., category (mathematics) focusing on more theorems and basic notions, and less on definitions and terminology. It is generally a bad idea to bombard readers with unfamiliar terms. -- Taku 07:05, August 6, 2005 (UTC)

Contents 1 a/the - language question 2 Construct/concrete category 3 Sorting 4 2007-02-1 Automated pywikipediabot message 5 A quasicategory is not a category

[edit] a/the - language question

I'm not a native speaker, but:

CAT is the quasicategory of all categories

sounds imho better than.

CAT is a quasicategory of all categories

--Kompik 15:13, 20 February 2006 (UTC)

[edit] Construct/concrete category

The book Abstract and Concrete Categories uses construct in the same meaning as concrete category is used in the glossary. (Construct is a concrete category over Set - Definition 5.1) --Kompik 15:13, 20 February 2006 (UTC)

[edit] Sorting

All sections apart from the first are alphabetically sorted. I cannot see the reason why the items in the first section are ordered in this way. --Kompik 15:16, 20 February 2006 (UTC)

[edit] 2007-02-1 Automated pywikipediabot message

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[edit] A quasicategory is not a category

The article says "A category A is said to be: ... quasicategory provided that objects in A may not form a class and morphisms between objects A and B may not form a set". If the objects do not form a class and Mor(A,B) does not form a set, the thing is not a category. The definition of "quasicategory" should be moved out to its own paragraph. —Preceding unsigned comment added by 83.250.109.195 (talk) 18:10, 5 March 2008 (UTC)

Hi. This is confusing because "class" means something different in different formalisms, and so "category" means something different in different formalisms. Herrlich and Strecker assume the collection of all classes form a "conglomerate". This is a reasonable foundation, but I don't think it is standard. I think the following is fair: What AHS call "category", others would call "large category"; what they call "quasi-category" corresponds roughly to what others would call "super-large category", or perhaps "category in the third Grothendieck universe". (I wonder if the "quasi" terminology may be too specific to warrant listing here at all.) Sam (talk) 15:45, 28 September 2008 (UTC)

The discussion of "size" currently resides at Category of sets. Perhaps the AHS definition of "quasicategory" should be moved there… Sam (talk) 15:50, 28 September 2008 (UTC)