The coalgebraic enrichment of algebras in higher categories

@article{Peroux2020TheCE,
title={The coalgebraic enrichment of algebras in higher categories},
author={Maximilien P'eroux},
journal={arXiv: Algebraic Topology},
year={2020}
}
3 Citations
Coalgebras in the Dwyer-Kan localization of a model category
We show that weak monoidal Quillen equivalences induce equivalences of symmetric monoidal $\infty$-categories with respect to the Dwyer-Kan localization of the symmetric monoidal model categories.
Rigidification of connective comodules
We show that we can rigidify homotopy coherent comodules in connective modules over the Eilenberg-Mac Lane spectrum of a field, or more generally of a finite product of fields $\mathbb{k}$. That is,
Spanier-Whitehead duality for topological coHochschild homology.
• Mathematics
• 2020
Following the Nikolaus-Scholze approach to THH, we extend the definition of topological coHochschild homology (coTHH) of Hess-Shipley to $\infty$-categories. After this, we prove that coTHH of what

References

SHOWING 1-10 OF 35 REFERENCES
Stable $\infty$-Operads and the multiplicative Yoneda lemma
We construct for every $\infty$-operad $\mathcal{O}^\otimes$ with certain finite limits new $\infty$-operads of spectrum objects and of commutative group objects in $\mathcal{O}$. We show that these
A short course on $\infty$-categories
In this short survey we give a non-technical introduction to some main ideas of the theory of $\infty$-categories, hopefully facilitating the digestion of the foundational work of Joyal and Lurie.
Coalgebras in symmetric monoidal categories of spectra
• Mathematics
Homology, Homotopy and Applications
• 2019
We show that all coalgebras over the sphere spectrum are cocommutative in the category of symmetric spectra, orthogonal spectra, $\Gamma$-spaces, $\mathcal{W}$-spaces and EKMM $\mathbb{S}$-modules.
Coalgebras in the Dwyer-Kan localization of a model category
We show that weak monoidal Quillen equivalences induce equivalences of symmetric monoidal $\infty$-categories with respect to the Dwyer-Kan localization of the symmetric monoidal model categories.
Dualizing cartesian and cocartesian fibrations
• Mathematics
• 2014
In this technical note, we proffer a very explicit construction of the "dual cocartesian fibration" $p^{\vee}$ of a cartesian fibration $p$, and we show they are classified by the same functor to
Spanier-Whitehead duality for topological coHochschild homology.
• Mathematics
• 2020
Following the Nikolaus-Scholze approach to THH, we extend the definition of topological coHochschild homology (coTHH) of Hess-Shipley to $\infty$-categories. After this, we prove that coTHH of what
Yoneda lemma for enriched ∞-categories
• V. Hinich
• Mathematics