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 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 deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor galois-theory 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 manifolds 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 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 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).
    • CommentRowNumber1.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 21st 2022

    Started page.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 21st 2022
    • (edited Nov 21st 2022)

    Thanks for adding good stuff!

    On formatting:

    I have slightly adjusted the typesetting of the (co)limits by placing their indices below the arrow:

      $$
        A_{\square}[S]
        \;=\;
        \underset
          {\underset{ A'\subseteq A }{ \rightarrow }}
          {\lim}
        \;
        \underset
          {\underset{i}{\leftarrow}}
          {\lim}
        \;
        A'\big[S_{i}\big]
      $$
    

    By the way, just by enclosing technical terms in double square brackets, they get automatically hyperlinked to their respective entries, which is much of what the point of the wiki is about.

    This certainly works for basics like ring ([[ring]]), subring ([[subring]]), profinite integers ([[profinite integers]]) etc.

    For something like “condensed AA-modules” we can typeset as [[condensed module|condensed $A$-modules]] and then create an entry titled “condensed module”.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 21st 2022
    • (edited Nov 21st 2022)

    By the way, do you mean to write “derived \infty-category”, or is this rather just “\infty-category”?

    The question is whether you mean just the homotopy category. This matters later when the entry speaks about the map of hom-objects being an “isomorphism”. From looking (just) at Mann’s abstract, I suspect this is really meant to be an equivalence of hom-spaces (i.e. of hom-\infty-groupoids)?

    • CommentRowNumber4.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 21st 2022
    Thanks for the fixes! I think it should be "derived $\infty$-category" (i.e. complexes of modules) and not just $\infty$-category. This is discussed in page 15 of Mann's arxiv preprint. Mann further gives 1.3 of Lurie's Higher Algebra as reference.
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 21st 2022

    I see, thanks. So let’s say:

    … the (“derived”) \infty-category of chain complexes of

    with pointer to “(infinity,1)-category of chain complexes”.

    diff, v4, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 21st 2022

    and so I have expanded the “the canonical map … is an isomorphism” to:

    the canonical map of mapping objects … is an equivalence

    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 22nd 2022

    Added a brief sentence on globalization and added a section for coherent duality, to be filled in later.

    diff, v6, current

    • CommentRowNumber8.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 22nd 2022

    Added the statement of Theorem 11.1 (Coherent Duality) from Scholze’s Lectures on Condensed Mathematics. The statement is currently verbatim, and I am planning to make edits in the future to give it more context.

    diff, v8, current

    • CommentRowNumber9.
    • CommentAuthorAnton Hilado
    • CommentTimeNov 22nd 2022

    Added section on the six operations.

    diff, v8, current

    • CommentRowNumber10.
    • CommentAuthorAnton Hilado
    • CommentTime6 days ago

    Started a section on Mann’s application of solid modules.

    diff, v10, current

    • CommentRowNumber11.
    • CommentAuthorAnton Hilado
    • CommentTime6 days ago

    Added Zavyalov reference.

    diff, v10, current

    • CommentRowNumber12.
    • CommentAuthorAnton Hilado
    • CommentTime5 days ago

    Starting to add a little more detail for the six-functor formalism for solid modules. Will fill in more later.

    diff, v11, current

    • CommentRowNumber13.
    • CommentAuthorAnton Hilado
    • CommentTime5 days ago

    Added mention of Mann’s p-torsion Riemann-Hilbert correspondence.

    diff, v13, current

    • CommentRowNumber14.
    • CommentAuthorAnton Hilado
    • CommentTime5 days ago

    Added statement of Poincare duality, included some pinpoint references, and corrected some typos. Might add statement of Mann’s p-torsion Riemann-Hilbert correspondence later, however this needs definitions of phi-modules and overconvergent etale sheaves.

    diff, v13, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)