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}
}
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3 Citations

3 Citations

Coalgebras in the Dwyer-Kan localization of a model category
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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.
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
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
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.
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
    Advances in Mathematics
  • 2020
Enriched ∞-categories via non-symmetric ∞-operads
Sweedler Theory for (co)algebras and the bar-cobar constructions
We prove that the category of dg-coalgebras is symmetric monoidal closed and that the category of dg-algebras is enriched, tensored, cotensored and strongly monoidal over that of coalgebras. We apply…
A short course on ∞-categories
In this short survey we give a non-technical introduction to some main ideas of the theory of ∞-categories, hopefully facilitating the digestion of the foundational work of Joyal and Lurie. Besides…
...
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