Corpus ID: 195847914

# Homotopy-coherent algebra via Segal conditions

@article{Chu2019HomotopycoherentAV,
title={Homotopy-coherent algebra via Segal conditions},
author={Hongyi Chu and R. Haugseng},
journal={arXiv: Algebraic Topology},
year={2019}
}
• Published 2019
• Mathematics
• arXiv: Algebraic Topology
Many homotopy-coherent algebraic structures can be described by Segal-type limit conditions determined by an "algebraic pattern", by which we mean an $\infty$-category equipped with a factorization system and a collection of "elementary" objects; examples include $\infty$-categories, $(\infty,n)$-categories, $\infty$-operads, and algebras for an $\infty$-operad in spaces. We characterize the monads on presheaf $\infty$-categories that arise in this way as precisely the cartesian monads that are… Expand

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