Not signed in (Sign In)

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 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 mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum 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 set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory 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).
    • CommentRowNumber1.
    • CommentAuthoradeelkh
    • CommentTimeJan 7th 2015
    • (edited Jan 7th 2015)
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 7th 2015

    Thanks! Maybe it’s time for a new floating table of contents “dg-Categories”.

    • CommentRowNumber3.
    • CommentAuthoradeelkh
    • CommentTimeJan 25th 2015

    I did some reorganization of the references, cleaned up some of the old query boxes, and rewrote some of the introduction at dg-category.

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 9th 2015

    I fixed a dead link for Toen’s lecture notes. I think the earliest use of the notion is in Kelly’s paper from 1965. The terminology though is from much later and the development for applications other than homology theory as well.

    • CommentRowNumber5.
    • CommentAuthoradeelkh
    • CommentTimeFeb 9th 2015

    Thanks. I wonder if the idea of weak enrichment, i.e. enrichment up to quasi-isomorphism, is already present in that paper?

    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 9th 2015
    • (edited Feb 9th 2015)

    My reference to Kelly is from Keller and means enriched in (Ch(A),)(Ch(A),\otimes) or one of the bounded or semi-bounded variants. Weak enrichment is much later, I think. I don’t know if Jim Stasheff looks at that anywhere at that time.

    Some of Ross Street’s early papers were more in this chain complex setting than his later work would lead one to expect.

    • CommentRowNumber7.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 10th 2015

    Adeel, Is there (in the nLab or elsewhere) a good set of notes that explains the use of dg-categories in representation theory. I keep on seeing phrases that say how important an application it is but so far have not found a good introduction!

    • CommentRowNumber8.
    • CommentAuthoradeelkh
    • CommentTimeFeb 10th 2015

    I’m only aware of Keller’s survey, which if I recall correctly has some discussion of applications to representation theory. I’ll ask my friend Pieter Belmans if he has any recommendations.

    • CommentRowNumber9.
    • CommentAuthoradeelkh
    • CommentTimeFeb 10th 2015
    • (edited Feb 10th 2015)

    Pieter recommended Keller’s survey as well, specifically section 4.9 on orbit categories. He also mentioned that another interesting application is in this paper.

    • CommentRowNumber10.
    • CommentAuthorTim_Porter
    • CommentTimeFeb 10th 2015

    Thanks (and thanks to Pieter). I will take a look.

    • CommentRowNumber11.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 16th 2018

    What happened to dg-category? The current page has removed all content from rev 41. Did we rename it?

    • CommentRowNumber12.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 17th 2018

    Ah, from the last diff page, Zoran added a reference and changed a subtitle. Why isn’t the entry showing?

  1. Made it render now. Problem was that the page tried to include ’homological algebra - contents’, which apparently does not exist. Later I can check if there is some other variant of this contents page which was intended.

    • CommentRowNumber14.
    • CommentAuthorRichard Williamson
    • CommentTimeAug 17th 2018
    • (edited Aug 17th 2018)

    The page homological algebra - contents does exist, I have now added it back to dg-category (there must have been a typo or something before), and fixed a link.

    • CommentRowNumber15.
    • CommentAuthorTim_Porter
    • CommentTimeApr 19th 2023

    Fixed link to Tabuada’s thesis.

    diff, v47, current

    • CommentRowNumber16.
    • CommentAuthorperezl.alonso
    • CommentTimeMay 14th 2024
    • (edited May 14th 2024)


    • Yuki Imamura. A formal categorical approach to the homotopy theory of dg categories (2024). (arXiv:2405.07873).

    diff, v48, current