Homotopy diagrams of algebras

Markl, Martin. "Homotopy diagrams of algebras." Proceedings of the 21st Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2002. [161]-180. <http://eudml.org/doc/221412>.

@inProceedings{Markl2002,
abstract = {The paper is concerned with homotopy concepts in the category of chain complexes. It is part of the author’s program to translate [J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lect. Notes Math. 347, Springer-Verlag (1973; Zbl 0285.55012)] from topology to algebra.In topology the notion of operad extracts the essential algebraic information contained in the following example (endomorphism operad).The endomorphism operad $\{\mathcal \{E\}\}_X$ of a based space $X$ consists of the family $\{\mathcal \{E\}\}_X(j)$$(j\ge 0)$ of spaces of based maps $X^j\rightarrow X$, together with the collection of continuous maps \[\gamma :\{\mathcal \{E\}\}\_X(k)\times \{\mathcal \{E\}\}\_X(j\_1)\times \cdots \times \{\mathcal \{E\}\}\_X(j\_k)\rightarrow \{\mathcal \{E\}\}\_X(j)\] given by the formula \[\gamma (f; g\_1,\dots , g\_k)= f(g\_1\times \cdots \times g\_k),\] where $k,j_1,\dots , j_k,j$ are such that $j= \sum ^k_\{s=1\} j_s$.Operads have proved to be a convenient tool to investigate, for example!},
author = {Markl, Martin},
booktitle = {Proceedings of the 21st Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {[161]-180},
publisher = {Circolo Matematico di Palermo},
title = {Homotopy diagrams of algebras},
url = {http://eudml.org/doc/221412},
year = {2002},
}

TY - CLSWK
AU - Markl, Martin
TI - Homotopy diagrams of algebras
T2 - Proceedings of the 21st Winter School "Geometry and Physics"
PY - 2002
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [161]
EP - 180
AB - The paper is concerned with homotopy concepts in the category of chain complexes. It is part of the author’s program to translate [J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lect. Notes Math. 347, Springer-Verlag (1973; Zbl 0285.55012)] from topology to algebra.In topology the notion of operad extracts the essential algebraic information contained in the following example (endomorphism operad).The endomorphism operad ${\mathcal {E}}_X$ of a based space $X$ consists of the family ${\mathcal {E}}_X(j)$$(j\ge 0)$ of spaces of based maps $X^j\rightarrow X$, together with the collection of continuous maps \[\gamma :{\mathcal {E}}_X(k)\times {\mathcal {E}}_X(j_1)\times \cdots \times {\mathcal {E}}_X(j_k)\rightarrow {\mathcal {E}}_X(j)\] given by the formula \[\gamma (f; g_1,\dots , g_k)= f(g_1\times \cdots \times g_k),\] where $k,j_1,\dots , j_k,j$ are such that $j= \sum ^k_{s=1} j_s$.Operads have proved to be a convenient tool to investigate, for example!
KW - Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/221412
ER -