Forests and the W Construction
Justin D Thomas
TL;DR
This paper refines the category of forests to analyze the W construction for colored operads, demonstrating cofibration properties and applying the framework to the swiss cheese operad, showing its equivalence to certain substructures.
Contribution
It introduces a modified forest category and uses it to establish cofibration properties of the W construction for colored operads, with applications to the swiss cheese operad.
Findings
The modified forest category simplifies analysis of the W construction.
The cofibration properties are established for colored operads.
The swiss cheese operad is shown to be equivalent to its degree 0 and 1 parts.
Abstract
A modified definition of the category of forests by Costello and expounded upon by Getzler is given. This language is used to prove some cofibration properties of the W construction for colored operads, following the work of Berger-Moerdijk. An application is given to the swiss cheese operad. The language of forests is convenient for showing that the swiss cheese operad is equivalent to its free degree 0 and 1 pieces.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology