# Derived bracket construction up to homotopy and Schroder numbers

Source: [Derived bracket construction up to homotopy and Schroder numbers](<https://www.sota2.com/research/paper/68fa50081e209131ce968267>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:37:38.501Z

Authors: K. Uchino

Published: 2012-02-01T04:31:59.000Z

## Abstract

We will introduce the notion of higher derived bracket construction in the category of operads and prove that the higher derived bracket construction of Lie operad is equivalent to the cobar construction of Leibniz operad. The theorem is proved by computing Schroder number.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1202.0095>)

[PDF](<https://arxiv.org/pdf/1202.0095.pdf>)