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 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 finite 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 integration integration-theory internal-categories itex k-theory lie lie-theory limit 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 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 string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory 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).
    • New stubs Oka principle, Oka manifold (with redirect Oka map) and Franc Forstnerič. Jardine has shown that one can use the Toen-Vezzosi like engineering with his intermediate model structure on the category of simplicial presheaves on a simplicial version of the Stein site. The (,1)(\infty,1)-stacks/fibrants will be Oka maps; those cofibrants which are represented by complex manifolds are in fact Stein manifolds.

    • I expanded some entries related to the Café-discussion:

      • at over-(infinity,1)-topos I expanded the Idea-section, added a few remarks on proofs and polished a bit,

        and added the equivalence Grpd/XPSh (X)\infty Grpd/X \simeq PSh_{\infty}(X) to the Examples-section

      • at base change geometric morphism I restructured the entry a little and then included the proof of the existence of the base change geometric morphism

    • added to adjunct the description in terms of units and counits.

    • created (infinity,1)-algebraic theory.

      I tried to adapt Rosicky’s and Lurie’s terminology such as to match that at algebraic theory, but Mike, Toby, Todd and whoever else feels expert should please check if I did it right.

    • New reference entry FAC aka Faisceaux algébriques cohérents. And few improvements to coherent sheaf including historical note.

    • added the equivalence

      Top/XSh (,1)(X) Top/X \simeq Sh_{(\infty,1)}(X)

      here

    • Kevin Walker was so kind to add a bit of material to blob homology. Notably he added a link to a set of notes now available that has more details.

      I added formatting and some hyperlinks.

    • I added to loop space a reference to Jim’s classic article, which was only linked to from H-space and put pointers indicating that his delooping result in TopTop is a special case of a general statement in any \infty-topos.

      By the way: it seems we have slight collision of terminology convention here: at “loop space” it says that H-spaces are homotopy associative, but at “H-space” only a homotopy-unital binary composition is required, no associativity. I think this is the standard use. I’d think we need to modify the wording at loop space a little.

    • I reworked A-infinity algebra so as to apply to algebras over any A A_\infty-operad in any ambient category. So I created subsections “In chain complexes”, “In topological spaces”.

      I think if we speak generally of “algebra over an operad” then we should also speak generally of “A A_\infty-algebra” even if the enriching category is not chain complexes. Otherwise it will become a mess. But I did link to A-infinity space.

    • added the definition of “coloured operad” to operad in the section “Rough definition”

      (by the way, should we not rather call these “pedestrian definition” or so instead of “rough”? The latter seems to suggest that there is something not quite working yet with these definitions, while in fact they are perfectly fine, just not as high-brow as other definitions.)

    • I started an idea section at transgression, but it could probably use some going over by an expert. I hope I didn’t mess things up too badly. I was reading Urs’ note on “integration without integration” on the train ride home and fooled myself into thinking I understood something.

      By the way, this reminded me of a discussion we had a while back

      Integrals: Loops space vs target space