Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 finite 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 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

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 16th 2019
   • (edited Oct 16th 2019)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * [[Dev Sinha]], Section 1 in: _Koszul duality in algebraic topology - an historical perspective_, J. Homotopy Relat. Struct. (2013) 8: 1 ([arXiv:1001.2032](https://arxiv.org/abs/1001.2032)) <a href="https://ncatlab.org/nlab/revision/diff/bar+and+cobar+construction/22">diff</a>, <a href="https://ncatlab.org/nlab/revision/bar+and+cobar+construction/22">v22</a>, <a href="https://ncatlab.org/nlab/show/bar+and+cobar+construction">current</a>

   added pointer to

   • Dev Sinha, Section 1 in: Koszul duality in algebraic topology - an historical perspective, J. Homotopy Relat. Struct. (2013) 8: 1 (arXiv:1001.2032)

   diff, v22, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 16th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * [[Yves Felix]], [[Stephen Halperin]], [[Jean-Claude Thomas]], _Adams' Cobar Equivalence_, Transactions of the American Mathematical Society Vol. 329, No. 2 (1992), pp. 531-549 ([jstor:2153950](https://www.jstor.org/stable/2153950)) <a href="https://ncatlab.org/nlab/revision/diff/bar+and+cobar+construction/22">diff</a>, <a href="https://ncatlab.org/nlab/revision/bar+and+cobar+construction/22">v22</a>, <a href="https://ncatlab.org/nlab/show/bar+and+cobar+construction">current</a>

   added pointer to

   • Yves Felix, Stephen Halperin, Jean-Claude Thomas, Adams’ Cobar Equivalence, Transactions of the American Mathematical Society Vol. 329, No. 2 (1992), pp. 531-549 (jstor:2153950)

   diff, v22, current

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 16th 2019
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexRe #1, the connection with this page goes via Koszul duality of the associative operad?

   Re #1, the connection with this page goes via Koszul duality of the associative operad?

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeOct 16th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexThat's true, but also the first half (Section 1) of the article is explicitly about bar/cobar construction and their relation. So I have added a "Section 1 in:..." to the reference item.

   That’s true, but also the first half (Section 1) of the article is explicitly about bar/cobar construction and their relation.

   So I have added a “Section 1 in:…” to the reference item.

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 16th 2019
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexIt would be good to add a line about the connection. What is it? That the adjunction between the bar and cobar constructions is (a consequence of) Koszul duality for the associative operad?

   It would be good to add a line about the connection. What is it? That the adjunction between the bar and cobar constructions is (a consequence of) Koszul duality for the associative operad?

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeOct 21st 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to the recent * Rivera, _Adams' cobar construction revisited_ ([arxiv:1910.08455](https://arxiv.org/abs/1910.08455)) <a href="https://ncatlab.org/nlab/revision/diff/bar+and+cobar+construction/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/bar+and+cobar+construction/26">v26</a>, <a href="https://ncatlab.org/nlab/show/bar+and+cobar+construction">current</a>

   added pointer to the recent

   • Rivera, Adams’ cobar construction revisited (arxiv:1910.08455)

   diff, v26, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeSep 20th 2022
   • (edited Sep 20th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Manuel Rivera]], [[Mahmoud Zeinalian]], *Cubical rigidification, the cobar construction, and the based loop space*, Algebr. Geom. Topol. **18** (2018) 3789-3820 &lbrack;[arXiv:1612.04801](https://arxiv.org/abs/1612.04801), [doi:10.2140/agt.2018.18.3789](https://doi.org/10.2140/agt.2018.18.3789)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/bar+and+cobar+construction/28">diff</a>, <a href="https://ncatlab.org/nlab/revision/bar+and+cobar+construction/28">v28</a>, <a href="https://ncatlab.org/nlab/show/bar+and+cobar+construction">current</a>

   added pointer to:

   • Manuel Rivera, Mahmoud Zeinalian, Cubical rigidification, the cobar construction, and the based loop space, Algebr. Geom. Topol. 18 (2018) 3789-3820 [arXiv:1612.04801, doi:10.2140/agt.2018.18.3789]

   diff, v28, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeSep 20th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[John Frank Adams]], *On the cobar construction*, Proc Natl Acad Sci USA **42** 7 (1956) 409–412 &lbrack;[doi:10.1073/pnas.42.7.409](https://doi.org/10.1073%2Fpnas.42.7.409)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/bar+and+cobar+construction/28">diff</a>, <a href="https://ncatlab.org/nlab/revision/bar+and+cobar+construction/28">v28</a>, <a href="https://ncatlab.org/nlab/show/bar+and+cobar+construction">current</a>

   added pointer to:

   • John Frank Adams, On the cobar construction, Proc Natl Acad Sci USA 42 7 (1956) 409–412 [doi:10.1073/pnas.42.7.409]

   diff, v28, current

9. • CommentRowNumber9.
   • CommentAuthorzskoda
   • CommentTimeJun 12th 2023
   • PermaLink
   Author: zskoda
   Format: MarkdownItex* [[Mathieu Anel]], [[André Joyal]], _On the bar-cobar duality for algebras and operads_, slides 2012, [pdf](http://mathieu.anel.free.fr/mat/doc/Anel-Joyal-Boston-Operades.pdf) * [[Kathryn Hess]], _The cobar construction: a modern perspective_, lectures 2007, [pdf](https://sma.epfl.ch/~hessbell/Minicourse_Louvain_Notes.pdf) <a href="https://ncatlab.org/nlab/revision/diff/bar+and+cobar+construction/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/bar+and+cobar+construction/30">v30</a>, <a href="https://ncatlab.org/nlab/show/bar+and+cobar+construction">current</a>

   • Mathieu Anel, André Joyal, On the bar-cobar duality for algebras and operads, slides 2012, pdf
   • Kathryn Hess, The cobar construction: a modern perspective, lectures 2007, pdf

   diff, v30, current