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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 18th 2011
    • (edited Nov 18th 2011)

    have created a “floating TOC” notions of subcategory and have included it in the relevant entries

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeNov 19th 2011
    • (edited Nov 19th 2011)

    Maybe a better and simpler title would be simply “subcategories” (this is a topic and it is potentially a bit wider than listing kinds of subcategories, for example it would include torsion theory which is a couple of subcategories satisfying some axioms). I think we also have entry thick subcategory.

    But here is somewhat related genuine question, not for subcategories but subfunctors. There is something I called in one paper “equivalence of subfunctors” and I did not know the standard term. Maybe somebody does ? So let F 1,F 2:ABF_1,F_2:A\to B be subfunctors of a functor G:ABG:A\to B in which BB is a category with images. We say that F 1F_1 is equivalent to F 2F_2 if there is a natural automorphism α:GG\alpha:G\Rightarrow G such that for every aOb(A)a\in Ob(A) the restriction α a| ImF 1(a)\alpha_a|_{Im F_1(a)} is isomorphism onto ImF 2(a)Im F_2(a). Thus, roughly speaking there is an natural isomorphism of functors F 1F 2F_1\cong F_2 which extends to a natural automorphism of GG.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 19th 2011
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMar 27th 2023

    added bireflective subcategory and touched the formatting of the first few lines

    diff, v10, current