Please note: You are viewing the unstyled version of this web site. Either your browser does not support CSS (cascading style sheets) or it has been disabled.

Macquarie University  Department of Mathematics

Local Navigation

Categories in Algebra, Geometry and Mathematical Physics

Conference in honour of Ross Street's sixtieth birthday

July 11-16 2005, Macquarie University, Sydney

Wed, 13 July:  10:45 - 11:25

Bimodules over operads: encoding deep structure of morphisms
Scott, Jonathan (École Polytechnique Fédèrale de Lausanne)

\thanks{Joint work with K.\ Hess (EPFL) and P.-E.\ Parent (U. Ottawa).}
An operad $P$ determines a category of $P$-algebras and their morphisms. The algebras and morphisms are linked, in the sense that in order to alter the morphisms, one must alter $P$, changing the algebras in the process.

We will show how $P$-bimodules can be used to give more freedom in describing morphisms. Let $R$ be a $P$-bimodule. If $R$ is a $P$-cooperad, then the category of $P$-algebras and ``$R$-relative" morphisms is a full subcategory of the Kleisli category for the triple associated to $R$. We apply this idea to unravel the algebraic structure in morphisms of bar/cobar constructions.

As a concrete example, we construct a bimodule over the associative operad of chain complexes that yields the category of associative algebras and ``strongly homotopy-multiplicative" morphisms.

Typeset PDF of this abstract.