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1. • CommentRowNumber1.
   • CommentAuthorKeith J. Bauer
   • CommentTime6 days ago
   • PermaLink
   Author: Keith J. Bauer
   Format: MarkdownItexHi, I am new here so please excuse any formatting errors. I am looking for a reference on what I do not have a term for so I will call it subobject philosophy. What I mean is that the "right" definition of subobject often depends on the category. Broadly, it is generally agreed that subobjects should be _at most_ monomorphisms (up to slice isomorphism) and _at least_ regular monomorphisms. However, I have gotten this information purely from a friend and I wish to fact-check it. Is there any article about this or similar on the nLab or elsewhere? I do see mention of these concepts on their relevant pages, but no article pointedly about the "philosophy" of how one chooses which to use, or a compilation of the list of criteria currently in use across various categories. Thank you all for your time.

   Hi, I am new here so please excuse any formatting errors.

   I am looking for a reference on what I do not have a term for so I will call it subobject philosophy. What I mean is that the “right” definition of subobject often depends on the category. Broadly, it is generally agreed that subobjects should be at most monomorphisms (up to slice isomorphism) and at least regular monomorphisms. However, I have gotten this information purely from a friend and I wish to fact-check it. Is there any article about this or similar on the nLab or elsewhere? I do see mention of these concepts on their relevant pages, but no article pointedly about the “philosophy” of how one chooses which to use, or a compilation of the list of criteria currently in use across various categories.

   Thank you all for your time.