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 ${ℰ}_X$ of a based space $X$ consists of the family ${ℰ}_X\left(j\right)$ $(j\ge 0)$ of spaces of based maps $X^j\to X$, together with the collection of continuous maps $$\gamma :{ℰ}_X\left(k\right)\times {ℰ}_X\left(j_1\right)\times \cdots \times {ℰ}_X\left(j_k\right)\to {ℰ}_X\left(j\right)$$ given by the formula $$\gamma (f;g_1,\cdots ,g_k)=f(g_1\times \cdots \times g_k),$$ where $k,j_1,\cdots ,j_k,j$ are such that $j={\sum }_{s=1}^k{j}_s$.Operads have proved to be a convenient tool to investigate, for example!

EUDML-ID : urn:eudml:doc:221412
Mots clés:

@article{701787,
     title = {Homotopy diagrams of algebras},
     booktitle = {Proceedings of the 21st Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2002},
     pages = {[161]-180},
     mrnumber = {MR1972432},
     zbl = {1024.55012},
     url = {http://dml.mathdoc.fr/item/701787}
}

Markl, Martin. Homotopy diagrams of algebras, dans Proceedings of the 21st Winter School "Geometry and Physics", GDML_Books,  (2002), pp. [161]-180. http://gdmltest.u-ga.fr/item/701787/