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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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 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
   • CommentTimeAug 18th 2020
   • (edited Aug 18th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded doi and pointer to relevant sections to * Marcelo Aguilar, [[Samuel Gitler]], Carlos Prieto, section 6 of _Algebraic topology from a homotopical viewpoint_, Springer (2002) ([toc pdf](http://tocs.ulb.tu-darmstadt.de/106999419.pdf), [doi:10.1007/b97586](https://link.springer.com/book/10.1007/b97586)) > (EM-spaces are constructed in section 6, the cohomology theory they represent is discussed in section 7.1, and its equivalence to singular cohomology is Corollary 12.1.20) <a href="https://ncatlab.org/nlab/revision/diff/Eilenberg-Mac+Lane+space/25">diff</a>, <a href="https://ncatlab.org/nlab/revision/Eilenberg-Mac+Lane+space/25">v25</a>, <a href="https://ncatlab.org/nlab/show/Eilenberg-Mac+Lane+space">current</a>

   Added doi and pointer to relevant sections to

   • Marcelo Aguilar, Samuel Gitler, Carlos Prieto, section 6 of Algebraic topology from a homotopical viewpoint, Springer (2002) (toc pdf, doi:10.1007/b97586)

     (EM-spaces are constructed in section 6, the cohomology theory they represent is discussed in section 7.1, and its equivalence to singular cohomology is Corollary 12.1.20)

   diff, v25, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 2nd 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the original references: *** Eilenberg-MacLane spaces originate with: * {#EilenbergMacLane53I} [[Samuel Eilenberg]], [[Saunders Mac Lane]], _On the Groups $H(\Pi,n)$, I_, Annals of Mathematics Second Series, Vol. 58, No. 1 (Jul., 1953), pp. 55-106 ([jstor:1969820](https://www.jstor.org/stable/1969820)) * {#EilenbergMacLane54II} [[Samuel Eilenberg]], [[Saunders Mac Lane]], _On the Groups $H(\Pi,n)$, II: Methods of Computation_, Annals of Mathematics Second Series, Vol. 60, No. 1 (Jul., 1954), pp. 49-139 ([jstor:1969702](https://www.jstor.org/stable/1969702)) * {#EilenbergMacLane54III} [[Samuel Eilenberg]], [[Saunders Mac Lane]], _On the Groups $H(\Pi,n)$, III: Operations and Obstructions_, Annals of Mathematics Second Series, Vol. 60, No. 3 (Nov., 1954), pp. 513-557 ([jstor:1969849](https://www.jstor.org/stable/1969849)) That Eilenberg-MacLane spaces represent [[ordinary cohomology]] is due to: * [[Samuel Eilenberg]], p. 243 of: _Cohomology and Continuous Mappings_, Annals of Mathematics Second Series, Vol. 41, No. 1 (Jan., 1940), pp. 231-251 ([jstor:1968828](https://www.jstor.org/stable/1968828)) * [Eilenberg-MacLane 54 III, p. 520-521](#EilenbergMacLane54III) Early review is in * [[Norman Steenrod]], Section 19 of: _Cohomology operations, and obstructions to extending continuous functions_ Advances in Math. 8, 371&#8211;416. (1972) (<a href="https://doi.org/10.1016/0001-8708(72)90004-7">doi:10.1016/0001-8708(72)90004-7</a>, [pdf](http://www.maths.ed.ac.uk/%7Eaar/papers/steen6.pdf)) *** <a href="https://ncatlab.org/nlab/revision/diff/Eilenberg-Mac+Lane+space/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/Eilenberg-Mac+Lane+space/26">v26</a>, <a href="https://ncatlab.org/nlab/show/Eilenberg-Mac+Lane+space">current</a>

   added the original references:

   ---

   Eilenberg-MacLane spaces originate with:

   • {#EilenbergMacLane53I} Samuel Eilenberg, Saunders Mac Lane, On the Groups $H(\Pi,n)$, I, Annals of Mathematics Second Series, Vol. 58, No. 1 (Jul., 1953), pp. 55-106 (jstor:1969820)

   • {#EilenbergMacLane54II} Samuel Eilenberg, Saunders Mac Lane, On the Groups $H(\Pi,n)$, II: Methods of Computation, Annals of Mathematics Second Series, Vol. 60, No. 1 (Jul., 1954), pp. 49-139 (jstor:1969702)

   • {#EilenbergMacLane54III} Samuel Eilenberg, Saunders Mac Lane, On the Groups $H(\Pi,n)$, III: Operations and Obstructions, Annals of Mathematics Second Series, Vol. 60, No. 3 (Nov., 1954), pp. 513-557 (jstor:1969849)

   That Eilenberg-MacLane spaces represent ordinary cohomology is due to:

   • Samuel Eilenberg, p. 243 of: Cohomology and Continuous Mappings, Annals of Mathematics Second Series, Vol. 41, No. 1 (Jan., 1940), pp. 231-251 (jstor:1968828)

   • Eilenberg-MacLane 54 III, p. 520-521

   Early review is in

   • Norman Steenrod, Section 19 of: Cohomology operations, and obstructions to extending continuous functions Advances in Math. 8, 371–416. (1972) (doi:10.1016/0001-8708(72)90004-7, pdf)

   ---

   diff, v26, current

3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeSep 2nd 2020
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexIt is good to have the original references and, where feasible, to have them linked.

   It is good to have the original references and, where feasible, to have them linked.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 24th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added publication data and DOI to: * [[Dan Licata]], [[Eric Finster]], _Eilenberg-MacLane spaces in homotopy type theory_, CSL-LICS '14 **66** (2014) 1-9 $[$[pdf text](http://dlicata.web.wesleyan.edu/pubs/lf14em/lf14em.pdf), [Agda HoTT code](https://github.com/dlicata335/hott-agda/blob/master/homotopy/KGn.agda), [web discussion](http://homotopytypetheory.org/2014/04/15/eilenberg-maclane-spaces-in-hott/), [doi:10.1145/2603088.2603153](https://doi.org/10.1145/2603088.2603153)$]$ <a href="https://ncatlab.org/nlab/revision/diff/Eilenberg-Mac+Lane+space/32">diff</a>, <a href="https://ncatlab.org/nlab/revision/Eilenberg-Mac+Lane+space/32">v32</a>, <a href="https://ncatlab.org/nlab/show/Eilenberg-Mac+Lane+space">current</a>

   I have added publication data and DOI to:

   • Dan Licata, Eric Finster, Eilenberg-MacLane spaces in homotopy type theory, CSL-LICS ’14 66 (2014) 1-9 $[$pdf text, Agda HoTT code, web discussion, doi:10.1145/2603088.2603153$]$

   diff, v32, current

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 14th 2023
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded * David Wärn, _Eilenberg-MacLane spaces and stabilisation in homotopy type theory_ ([arXiv:2301.03685](https://arxiv.org/abs/2301.03685)) <a href="https://ncatlab.org/nlab/revision/diff/Eilenberg-Mac+Lane+space/36">diff</a>, <a href="https://ncatlab.org/nlab/revision/Eilenberg-Mac+Lane+space/36">v36</a>, <a href="https://ncatlab.org/nlab/show/Eilenberg-Mac+Lane+space">current</a>

   Added

   • David Wärn, Eilenberg-MacLane spaces and stabilisation in homotopy type theory (arXiv:2301.03685)

   diff, v36, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJan 20th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Ulrik Buchholtz]], [[J. Daniel Christensen]], [[Jarl G. Taxerås Flaten]], [[Egbert Rijke]], *Central H-spaces and banded types* &lbrack;[arXiv:2301.02636](https://arxiv.org/abs/2301.02636)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Eilenberg-Mac+Lane+space/38">diff</a>, <a href="https://ncatlab.org/nlab/revision/Eilenberg-Mac+Lane+space/38">v38</a>, <a href="https://ncatlab.org/nlab/show/Eilenberg-Mac+Lane+space">current</a>

   added pointer to:

   • Ulrik Buchholtz, J. Daniel Christensen, Jarl G. Taxerås Flaten, Egbert Rijke, Central H-spaces and banded types [arXiv:2301.02636]

   diff, v38, current

7. • CommentRowNumber7.
   • CommentAuthorperezl.alonso
   • CommentTimeAug 23rd 2023
   • PermaLink
   Author: perezl.alonso
   Format: MarkdownItexadded couple of low-degree results of cohomology of EM spaces <a href="https://ncatlab.org/nlab/revision/diff/Eilenberg-Mac+Lane+space/39">diff</a>, <a href="https://ncatlab.org/nlab/revision/Eilenberg-Mac+Lane+space/39">v39</a>, <a href="https://ncatlab.org/nlab/show/Eilenberg-Mac+Lane+space">current</a>

   added couple of low-degree results of cohomology of EM spaces

   diff, v39, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJan 31st 2024
   • (edited Jan 31st 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded publication data for: * [[David Wärn]], *Eilenberg-MacLane spaces and stabilisation in homotopy type theory*, J. Homotopy Relat. Struct. **18** (2023) 357–368 &lbrack;[arXiv:2301.03685](https://arxiv.org/abs/2301.03685), [doi:10.1007/s40062-023-00330-5](https://doi.org/10.1007/s40062-023-00330-5)&rbrack; Am also copying a bunch of bibitems from here to *[[Eilenberg-MacLane space type]]*. <a href="https://ncatlab.org/nlab/revision/diff/Eilenberg-Mac+Lane+space/40">diff</a>, <a href="https://ncatlab.org/nlab/revision/Eilenberg-Mac+Lane+space/40">v40</a>, <a href="https://ncatlab.org/nlab/show/Eilenberg-Mac+Lane+space">current</a>

   added publication data for:

   • David Wärn, Eilenberg-MacLane spaces and stabilisation in homotopy type theory, J. Homotopy Relat. Struct. 18 (2023) 357–368 [arXiv:2301.03685, doi:10.1007/s40062-023-00330-5]

   Am also copying a bunch of bibitems from here to Eilenberg-MacLane space type.

   diff, v40, current

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeNov 21st 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Anatoly Fomenko]], [[Dmitry Fuchs]], §11.7-8 & p 263 in: *Homotopical Topology*, Graduate Texts in Mathematics **273**, Springer (2016) \[<a href="https://doi.org/10.1007/978-3-319-23488-5">doi:10.1007/978-3-319-23488-5</a>, <a href="https://www.cimat.mx/~gil/docencia/2020/topologia_diferencial/[Fomenko,Fuchs]Homotopical_Topology(2016).pdf">pdf</a>\] <a href="https://ncatlab.org/nlab/revision/diff/Eilenberg-Mac+Lane+space/41">diff</a>, <a href="https://ncatlab.org/nlab/revision/Eilenberg-Mac+Lane+space/41">v41</a>, <a href="https://ncatlab.org/nlab/show/Eilenberg-Mac+Lane+space">current</a>

   added pointer to:

   • Anatoly Fomenko, Dmitry Fuchs, §11.7-8 & p 263 in: Homotopical Topology, Graduate Texts in Mathematics 273, Springer (2016) [doi:10.1007/978-3-319-23488-5, pdf]

   diff, v41, current