| Title:
|
A finitely presented $E_infty$-prop I: Algebraic context (English) |
| Author:
|
Medina-Mardones, Anibal M. |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
4 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
1-21 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce a finitely presented prop $\mathcal{S}=\{\mathcal{S}(n,m)\}$ in the category of differential graded modules whose associated operad $U \mathcal{(S)}=\{\mathcal{S}(1,m)\}$ is a model for the $E_\infty$-operad. This finite presentation allows us to describe a natural $E_\infty$-coalgebra structure on the chains of simplicial sets in terms of only three maps: the Alexander-Whitney diagonal, the augmentation map, and an algebraic version of the join of simplices. The first appendix connects our construction to the Surjection operad of McClure-Smith and Berger-Fresse. The second establishes a duality between the diagonal and join maps for chains of augmented and non-augmented simplicial sets. A follow up paper [MM18b] constructs a prop corresponding to $\mathcal{S}$ in the category of $CW$-complexes. (English) |
| Keyword:
|
Operads |
| Keyword:
|
Props |
| Keyword:
|
$E_\infty$-structures |
| Keyword:
|
Normalized chains |
| MSC:
|
18C10 |
| MSC:
|
18G55 |
| MSC:
|
55U10 |
| idZBL:
|
Zbl 1459.55010 |
| idMR:
|
MR4133162 |
| DOI:
|
10.21136/HS.2020.08 |
| . |
| Date available:
|
2026-03-12T08:53:40Z |
| Last updated:
|
2026-03-12 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153424 |
| . |
| Reference:
|
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| Reference:
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