Not signed in (Sign In)

Start a new discussion

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 bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar 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-theory subobject 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

Show all

211 to 240 of 7496

  1. <
  2. 1
  3. ...
  4. 4
  5. 5
  6. 6
  7. 7
  8. 8
  9. 9
  10. 10
  11. 11
  12. ...
  13. 250
  14. >

    • That term intro rule was probably all wrong (edit: thanks go to GuiGeek here). Also tried to consistently rename A => B, X => A.

      diff, v11, current

    • added below the very first definition at kernel a remark that spells out the universal property more explicitly. Also added mentioning of some basic examples.

    • This is the list from proof assistant – Examples, and was (incompleteky) copied by hand into related entries, but we should make it (as done hereby) a standalone to be !includeed under “Related concepts” in relevant entries

      All I did in editing was to group the proof assistants into “based on type/set theory” and “applicable to homotopy type theory”. Experts please hit “edit” and improve on it

      v1, current

    • expanded chain homotopy: added the usual non-commuting diagram, a discussion of chain homotopy equivalence and slightly expanded the description in terms of left homotopy

    • am starting something, but not done yet, nothing to be seen here for the moment

      v1, current

    • a stub, just for completeness of the list of proof assistants

      v1, current

    • A long time ago we had a discussion at graph about notions of morphism. I have written an article category of simple graphs which collects some properties of the category under one of those definitions (corresponding better, I think, to graph-theoretic practice).

    • starting something – not done yet, but need to save

      v1, current

    • added under “Selected writings” the articles cited elsewhere on the nLab

      diff, v2, current

    • a bare minimum, just to record the references

      v1, current

    • Added a bunch of material to inverse semigroup under subsections of “Properties”.

    • I just aadded a sentence about Yang-Mills theory to gauge group, but there are some aspects of that article I feel we might want to discuss:

      I don’t think that the statement “gauge groups encoded redundancies” of the mathematical description of the physics is correct. One hears this every now and then, and I suppose the idea is the observation that physical observables have to be in the trivial representation of the gauge group, but there is more to the gauge group than that.

      Notably Yang-Mills theory is a theory of connections on G-principal bundles. No mathematician would ever say that the group G in a G-principal bundle just encodes a redundancy of our descriptins of that bundle. And the reason is because it is true only locally: the thing is that BG={*→g∈G*}\mathbf{B}G = \{* \stackrel{g \in G}{\to} * \} has a single object and hence is connected , but it has higher homotopy groups, and that’s where all the important information encoded by the gauge group sits.

      So I would say that instead of being a redundancy of the description, instead the gauge group of Yang-Mills theory enocedes precisely the homotopy type of its moduli space. This is rather important.

      A different matter are global gauge symmetries such as those that the DHR-theory deals with.

    • Page created, but author did not leave any comments.

      v1, current

    • added to Yang-Mills instanton a discussion of instantons as tunnelings between Chern-Simons vacua.

    • Page created, but author did not leave any comments.

      v1, current

    • I noticed some inconsistencies in the section outline at algebraic theory, that must have come from different people editing different pieces and mixing up some global entry structure.

      I have briefly tried to reinstantiate consistent order. But the entry could probably do with somebody looking over in its entirety with an editor-hat on.

    • Added redirects and a description of other contributions.

      diff, v2, current

211 to 240 of 7496

  1. <
  2. 1
  3. ...
  4. 4
  5. 5
  6. 6
  7. 7
  8. 8
  9. 9
  10. 10
  11. 11
  12. ...
  13. 250
  14. >
Top of Page