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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

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- Discussion Type
- discussion topicdependent sum natural deduction - table
- Category Latest Changes
- Started by atmacen
- Comments 2
- Last comment by atmacen
- Last Active Sep 12th 2019

- Discussion Type
- discussion topickernel
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by RodMcGuire
- Last Active Sep 12th 2019

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.

- Discussion Type
- discussion topicproof assistants and formalization projects -- list
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Sep 12th 2019

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`!include`

ed under “Related concepts” in relevant entriesAll 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

- Discussion Type
- discussion topicADE singularity
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active Sep 12th 2019

Yesterday I had added some rough bits and pieces and some references to

*ADE singularity*, and cross-linked with relevant entries such as*ADE classification*and*M-theory on G2-manifolds*. But for the moment this remains a stub.

- Discussion Type
- discussion topicchain homotopy
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by mattecapu
- Last Active Sep 12th 2019

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

- Discussion Type
- discussion topicheterotic M-theory on ADE-orbifolds
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Sep 12th 2019

- Discussion Type
- discussion topicproof assistant
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by atmacen
- Last Active Sep 12th 2019

this MO comment made me realize that we didn’t have an entry

*proof assistant*, so I started one

- Discussion Type
- discussion topicArend
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 12th 2019

- Discussion Type
- discussion topicmanifold with boundary
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 11th 2019

added the statement (now this prop) that smooth manifolds with boundary are fully faithful in diffeological spaces, with pointer to Igresias-Zemmour 13, section 4.16.

Will add the same to

*diffeological space*.

- Discussion Type
- discussion topiccategory of simple graphs
- Category Latest Changes
- Started by Todd_Trimble
- Comments 66
- Last comment by Todd_Trimble
- Last Active Sep 11th 2019

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).

- Discussion Type
- discussion topicequation of state
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 11th 2019

- Discussion Type
- discussion topicQCD trace anomaly
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 11th 2019

- Discussion Type
- discussion topicO4-plane
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 10th 2019

- Discussion Type
- discussion topicJoël Scherk
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 10th 2019

- Discussion Type
- discussion topicScherk-Schwarz mechanism
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 10th 2019

- Discussion Type
- discussion topicinverse semigroup
- Category Latest Changes
- Started by Todd_Trimble
- Comments 8
- Last comment by zskoda
- Last Active Sep 9th 2019

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

- Discussion Type
- discussion topicdisplayed category
- Category Latest Changes
- Started by Mike Shulman
- Comments 3
- Last comment by jesuslop
- Last Active Sep 8th 2019

New page displayed category.

- Discussion Type
- discussion topicgauge group
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Urs
- Last Active Sep 8th 2019

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 $\mathbf{B}G = \{* \stackrel{g \in G}{\to} * \}$ 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.

- Discussion Type
- discussion topicDp-D(p+4)-brane bound state
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 7th 2019

- Discussion Type
- discussion topicYang-Mills instanton
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 7th 2019

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

- Discussion Type
- discussion topicD0-D4-brane bound state
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 7th 2019

am starting this for completeness, in the context of a more general entry

*Dp-D(p+4)-brane bound state*. Nothing much here yet

- Discussion Type
- discussion topicinhomogeneous cosmology
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Sep 7th 2019

started something. For the moment really just a glorified pointer to Buchert et al. 15 and putting Scharf 13 into perspective

- Discussion Type
- discussion topicE-infinity algebra
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Dmitri Pavlov
- Last Active Sep 6th 2019

stub for E-infinity algebra

- Discussion Type
- discussion topicSoichiro Fujii
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Sep 6th 2019

- Discussion Type
- discussion topicalgebraic theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by David_Corfield
- Last Active Sep 6th 2019

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.

- Discussion Type
- discussion topicRR-field tadpole cancellation
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by Urs
- Last Active Sep 6th 2019

started some bare minimum omn RR-field tadpole cancellation. Currently I am using this just to complement discussion at

*intersecting D-brane models*

- Discussion Type
- discussion topicJeff Smith
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Sep 5th 2019

- Discussion Type
- discussion topicD4-D8 brane bound state
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 5th 2019

just a stub for the moment, in order to have a place for recording relevant references, such as

- Horatiu Nastase,
*On Dp-Dp+4 systems, QCD dual and phenomenology*(arXiv:hep-th/0305069)

- Horatiu Nastase,

- Discussion Type
- discussion topicRR-field tadpole cancellation on toroidal orientifolds -- table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 5th 2019

am giving this table from the entry

*RR-field tadpole cancellation*its stand-alone entry, so that it may be`!include`

-ed into other relevant entries, such as at*intersecting D-brane model*

- Discussion Type
- discussion topicmonoid in a monoidal category
- Category Latest Changes
- Started by anqurvanillapy
- Comments 5
- Last comment by nLab edit announcer
- Last Active Sep 5th 2019