A spectral sequence for spaces of maps between operads

TL;DR

This paper introduces a spectral sequence framework to analyze the derived mapping space between simplicially enriched operads, providing a layered approximation method under mild conditions.

Contribution

It constructs a tower of fibrations that approximates the derived mapping space, with each stage simplifying the operadic operations considered.

Findings

Main theorem describes the layers of the tower.

Provides a systematic approach to approximate mapping spaces.

Applicable under mild conditions to simplicially enriched operads.

Abstract

We construct a tower of fibrations approximating the derived mapping space between two simplicially enriched operads subject to mild conditions. The n-th stage of the tower is obtained by neglecting operations with more than n inputs. The main theorem describes the layers of this tower.