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 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 nforum 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
    • CommentTimeApr 15th 2021

    added publication details for this reference:

    and am copying it over to compactly generated topological space, too

    diff, v54, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2021
    • (edited Apr 16th 2021)

    made more explicit the statement that all those notions of epimorphisms agree in regular categories (here)

    diff, v55, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 22nd 2021

    added (here) the example GrpGrp which prointer to where in Borceux this is discussed.

    diff, v59, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 8th 2021

    The fact that cgHauscgHaus is regular was mentioned in the references, but not in the list of Examples, which ended instead with the counter-example saying that TopTop is not regular.

    So I have added mentioning of cgHauscgHaus also in the list of examples, now here.

    diff, v60, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 9th 2021

    added pointer to:

    diff, v61, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 9th 2021
    • (edited Nov 9th 2021)

    I have fixed the (previously somewhat weird) referencing of the original text and added the DOI-link:

    diff, v63, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 10th 2021

    I have added (here) compactly generated GG-spaces to the list of examples.

    diff, v64, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJul 7th 2022

    added pointer to

    for the claim that every topos is regular. (Also added pointers to other references for this fact. see here)

    diff, v67, current

    • CommentRowNumber9.
    • CommentAuthormaxsnew
    • CommentTimeSep 15th 2022

    xref with allegories

    diff, v71, current

    • CommentRowNumber10.
    • CommentAuthorʇɐ
    • CommentTimeSep 4th 2023

    I’m not sure what definition 2.5 (A regular category is a finitely complete category with pullback-stable image factorizations.) is supposed to mean; should it be “a finitely complete category for which (regular epis, monos) is a stable factorization system” instead (cf. theorem 1.14 of Gran’s An introduction to regular categories)? (That’s less trivial than “pulling back the image of f yields another mono, and the pullback of f factors through it”.)

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeSep 4th 2023

    I see that this question came up before in MO:q/252815 with essentially the same clarification proposed there in MO:252842.

    Since the originator of the nLab wording didn’t object there, I went ahead and added the clarification (here).

    diff, v75, current