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 definitions 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 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).

nLab > Latest Changes: Query at [[2-pullback]]

Bottom of Page

1 to 12 of 12

  1.  
    • CommentRowNumber1.
    • CommentAuthorTobyBartels
    • CommentTimeNov 15th 2009

    Zoran has already reported a query at 2-pullback, but I think that it should have wider exposure. I attempted a response.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeNov 15th 2009

    Same here. Possibly the "idea" section should say more about the possible sources of confusion, but I think it is correct as stated, with the default meanings of words on the nLab.

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeNov 15th 2009
    • (edited Nov 15th 2009)
    I have further argued for my point in 2-pullback. I also complaint about definitions at H-space, including wrong attribution to Stasheff. The original (Serre 1951 publication) notion of H-space does not include coherences, like in 1963 Stasheff or infty-groups of 200x Lurie. H-group is by a definition a group up to homotopy, not necessarily coherent homotopy. I added to the entry lots of details, references and variations in terminology. Of course I may be further corrected. Please look.

    I also notice that if I reedit some old comment in n-Forum it does not change its status. The n-Forum software reports the time of the last edit, as of when the first version of the entry was submitted. Thus updates within the same entry; by entry I mean the very comment, not the chain of comments. I think corrections to old comments could be dated when they were corrected, what the others think?
    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeNov 15th 2009

    I agree with you about dates; or rather, after the Comment Time, where it says ‘edited’ it should say when edited too. That way we get the time of both the original and of the last edit.

    Edited comments also don't count as unread; I try never to edit them unless I've just posted them and see a typo or something (or maybe to cross something out).

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeNov 15th 2009

    I put the stuff about time of last edit in a new thread so Andrew will see it.

    I also replied at 2-pullback and asked a question at H-space.

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeNov 15th 2009
    It says that you are editing 2-pullback already for 23 minutes so I am not toucing it. But I do not buy your argument. If you take cones on 3 vertex version, with arrows to A, B, and C, then the 2-limiting cone will be in some sense symmetric between A and B. So it is not to expect that it will have representatatives which have one 2-cell (the one via A) trivial, as by symmetry the other one would be trivial, so the cone would have no nontrivial cells at all ??
    • CommentRowNumber7.
    • CommentAuthorTobyBartels
    • CommentTimeNov 15th 2009
    • (edited Nov 15th 2009)

    Sorry, the edit is done now; I was distracted by other edits in the middle.

    There are many representatives for the cone, including one each in which each 2-cell is trivial, but usually none in which both are trivial.

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeNov 15th 2009
    • (edited Nov 15th 2009)
    The remark which you put in H-space about wikipedia definition (link needed) is I think not essential, I think there is a basic theorem if one has a magma in Top with homotopy unit, one can replace it with homotopy equivalent magma with strict unit. I think I have seen that claim somewhere in last few days, but I do not recall the place at the moment. Let us try to locate this if true it is useful to have this claim explicitly if true.
    • CommentRowNumber9.
    • CommentAuthorTobyBartels
    • CommentTimeNov 15th 2009

    I didn't put that remark in there; Urs did. (I just edited it.)

    But yes, that would be a good thing to track down. It sounds reasonable to me, like the idea that one can replace any weak \infty-category with one in which units are strict.

    • CommentRowNumber10.
    • CommentAuthorzskoda
    • CommentTimeNov 15th 2009
    What do you think about the entry deformation retract. It has a notion of deformation retract of model categories, but the classical situation which is in the paragraph which I describe is about a particular object in a fixed model category (say Top). So the two concepts are very different, though there is some analogy. Maybe we could think of two entries.

    As far as the weak units, I had some dreaming in last few days. There are so few references, mainly focusing on Simpson's conjecture but not much on applications. For example about crossed modules, and crossed complexes with weak units, nonabelian cohomology etc. Urs and I thought once on the possibility to work with coherent units instead but it seemed that the theory would be rather complicated (think for example on new coherences possible when you wisker the diagrams which have weak units) unlike the usual theory with weak units which seems to me somewhat simpler than the world of associators and alike. The new idea which occured to me this week is about weather one can model quasi-operads (which are usually modelled using dendroidal sets) with "operad with weak units" ?
    • CommentRowNumber11.
    • CommentAuthorMike Shulman
    • CommentTimeNov 20th 2009

    Going back to 2-pullback, I have greatly expanded the entry with a more careful explanation of why the two notions are the same (up to equivalence).

    • CommentRowNumber12.
    • CommentAuthorzskoda
    • CommentTimeNov 20th 2009
    Thanks a lot.

1 to 12 of 12

  1.