Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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

  1. Missing comma

    L Spice

    diff, v11, current