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}
}
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
Factorization systems in $\infty$-categories
Completeness for monads and theories
Higher Theories and Monads
The incidence comodule bialgebra of the Baez-Dolan construction

References

SHOWING 1-10 OF 30 REFERENCES
On the equivalence between Θ_{}-spaces and iterated Segal spaces
Enriched ∞-categories via non-symmetric ∞-operads
A Cellular Nerve for Higher Categories
Dendroidal Segal spaces and ∞-operads
The geometry of iterated loop spaces
Two models for the homotopy theory of ∞‐operads
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