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2-categories 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 connection constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality education elliptic-cohomology enriched fibration foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity 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 infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal-logic model model-category-theory monads monoid monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories 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 science set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

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- Discussion Type
- discussion topicvector G-space
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by DavidRoberts
- Last Active 19 minutes ago

Recording the result from Triantafillou 82, characterizing injective/projective objects in diagrams of vector spaces over (the opposite of) the orbit category.

(The degreewise ingredients in the rational model for topological G-spaces)

- Discussion Type
- discussion topicsimplicial principal bundle
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active 4 hours ago

am splitting off simplicial principal bundle from simplicial group

- Discussion Type
- discussion topiceffective quantum field theory
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active 5 hours ago

at effective quantum field theory I have started writing an Idea-section and added more reference

- Discussion Type
- discussion topichigher-order logic
- Category Latest Changes
- Started by David_Corfield
- Comments 2
- Last comment by NikolajK
- Last Active 13 hours ago

- Discussion Type
- discussion topicdagger category
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Tim Campion
- Last Active 20 hours ago

I took the liberty of incorporating material from Andre Joyal's latest message to the CatTheory mailing list into the entry dagger-category:

created sections

- Discussion Type
- discussion topiccofiber sequence
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 1 day ago

- Discussion Type
- discussion topicmodel structure for L-infinity algebras
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Urs
- Last Active 1 day ago

have started model structure for L-infinity algebras

- Discussion Type
- discussion topichierarchy problem
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 1 day ago

Added specific pointer to argument for solution of hierarchy problem due to Acharya-Kane-Kumar 12.

- Discussion Type
- discussion topicconvenient category of topological spaces
- Category Latest Changes
- Started by Todd_Trimble
- Comments 23
- Last comment by DavidRoberts
- Last Active 1 day ago

As I’ve already said elsewhere, I’ve been working on this entry and trying to give a precise definition based on my hunches of what guys like Steenrod really meant by “a convenient category of topological spaces”. (I must immediately admit that I’ve never read his paper with that title. Of course, he meant specifically compactly generated Hausdorff spaces, but nowadays I think we can argue more generally.)

I also said elsewhere that my proposed axiom on closed and open subspaces might be up for discussion. The other axioms maybe not so much: dropping any of them would seem to be a deal-breaker for what an algebraic topologist might consider “convenient”. Or so I think.

- Discussion Type
- discussion topicmodified Bernoulli number
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by nLab edit announcer
- Last Active 1 day ago

- Discussion Type
- discussion topicprojective resolution
- Category Latest Changes
- Started by Urs
- Comments 32
- Last comment by Urs
- Last Active 1 day ago

At

*projective resolution*I havespelled out the

*Definition*in lots of detail;spelled out statement and proof of the

*existence of resolutions*in full detail.

- Discussion Type
- discussion topicUrs Stammbach
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

brief

`category:people`

-entry for hyperlinking references at*homological algebra*

- Discussion Type
- discussion topicinjective envelope
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

added pointer to:

- Peter Hilton, Urs Stammbach, Section I.9 in:
*A course in homological algebra*, Springer-Verlag, New York, 1971, Graduate Texts in Mathematics, Vol. 4 (doi, pdf)

- Peter Hilton, Urs Stammbach, Section I.9 in:

- Discussion Type
- discussion topicThe Joy of Cats
- Category Latest Changes
- Started by DavidRoberts
- Comments 2
- Last comment by Urs
- Last Active 2 days ago

I edited The Joy of Cats to link to metacategory and to disambiguate quasicategory, as twice now someone on MO has used the term ’quasicategory’ to talk about (very) large categories. This way, if people find the book using the nLab page they are forewarned.

I also edited quasicategory to move the terminological warning up to the idea section where it is immediately visible, rather than in the second section, below the definition.

- Discussion Type
- discussion topicKan extension
- Category Latest Changes
- Started by Mike Shulman
- Comments 53
- Last comment by Urs
- Last Active 2 days ago

I think the line between the two types of Kan extension (weak versus pointwise) is drawn at the wrong place. Am I missing something?

- Discussion Type
- discussion topicequivariant Sullivan model
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicKähler manifold
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by nLab edit announcer
- Last Active 3 days ago

added publication data to

- Andrei Moroianu,
*Lectures on Kähler Geometry*, Cambridge University Press 2007 (arXiv:math/0402223 doi:10.1017/CBO9780511618666, pdf)

and pointer to section 11.1 there for Kaehler structures as torsion-free $U(n)$-structures

- Andrei Moroianu,

- Discussion Type
- discussion topicequivariant PL de Rham theorem
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicfundamental theorem of dg-algebraic equivariant rational homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 3 days ago

the equivariant generalization of the

*fundamental theorem of dg-algebraic rational homotopy theory*

- Discussion Type
- discussion topicequivariant homotopy type
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicQuillen adjunction between equivariant simplicial sets and equivariant connective dgc-algebras
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

the equivariant generalization of the

*Quillen adjunction between simplicial sets and connective dgc-algebras*

- Discussion Type
- discussion topicmodel structure on equivariant dgc-algebras
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 3 days ago

starting something, on

- Laura Scull,
*A model category structure for equivariant algebraic models*, Transactions of the American Mathematical Society 360 (5), 2505-2525, 2008 (doi:10.1090/S0002-9947-07-04421-2)

- Laura Scull,

- Discussion Type
- discussion topicmodel structure on equivariant chain complexes
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicequivariant chain complex
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicequivariant dgc-algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicequivariant PL de Rham complex
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

to go with

*PL de Rham complex*and with*dual vector G-space*.Not sure about the best terminology.

- Discussion Type
- discussion topicrational vector space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicWeyl group
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicChern character
- Category Latest Changes
- Started by Urs
- Comments 42
- Last comment by Urs
- Last Active 4 days ago

stub for Chern character

just the blind definition so far, to be expanded later

- Discussion Type
- discussion topicexponentiable topos
- Category Latest Changes
- Started by Thomas Holder
- Comments 4
- Last comment by Thomas Holder
- Last Active 4 days ago