13 papers
On products of skeleta
Liam Keenan, Maximilien Péroux
Given a symmetric monoidal -category , compatible with finite colimits, we show that the functor sending a simplicial object in to its skeletal f…
Functoriality of Enriched Data Types
Lukas Mulder, Paige Randall North, Maximilien Péroux
In previous work, categories of algebras of endofunctors were shown to be enriched in categories of coalgebras of the same endofunctor, and the extra structure of that enrichment w…
Coalgebraic -theory
Teena Gerhardt, Maximilien Péroux, W. Hermann B. Soré
We establish comparison maps between the classical algebraic -theory of algebras over a field and its analogue , an algebraic -theory for coalgebras over a field. The co…
Topological homology of rings with twisted -action
Gabriel Angelini-Knoll, Mona Merling, Maximilien Péroux
We construct topological -homology for rings with twisted -action. Here a ring with twisted -action is a common generalization of a ring with anti-involution and a ring w…
Measuring data types
Lukas Mulder, Paige Randall North, Maximilien Péroux
In this article, we combine Sweedler's classic theory of measuring coalgebras -- by which -algebras are enriched in -coalgebras for a field -- with the theory of W-types…
Equivariant algebraic -theory of symmetric monoidal Mackey functors
Maxine Calle, David Chan, Maximilien Péroux
We provide a unifying approach to different constructions of the algebraic -theory of equivariant symmetric monoidal categories. A consequence of our work is that every connecti…
Coinductive control of inductive data types
Paige Randall North, Maximilien Péroux
We combine the theory of inductive data types with the theory of universal measurings. By doing so, we find that many categories of algebras of endofunctors are actually enriched i…
A monoidal Dold-Kan correspondence for comodules
Maximilien Péroux
We provide examples of inductive fibrant replacements in fibrantly generated model categories constructed as Postnikov towers. These provide new types of arguments to compute homot…
The coalgebraic enrichment of algebras in higher categories
Maximilien Péroux
We prove that given a presentably symmetric monoidal -category, and any essentially small -operad , the -category of $\mathcal{O}…
Coalgebras in the Dwyer-Kan localization of a model category
Maximilien Péroux
We show that weak monoidal Quillen equivalences induce equivalences of symmetric monoidal -categories with respect to the Dwyer-Kan localization of the symmetric monoidal m…
Rigidification of connective comodules
Maximilien Péroux
Let be a commutative ring with global dimension zero. We show that we can rigidify homotopy coherent comodules in connective modules over the Eilenberg-Mac Lane spectr…
Koszul Duality in Higher Topoi
Jonathan Beardsley, Maximilien Péroux
We show that there is an equivalence in any -topos between the pointed and -connective objects of and the -group objects of the $(n-…
Coalgebras in symmetric monoidal categories of spectra
Maximilien Péroux, Brooke Shipley
We show that all coalgebras over the sphere spectrum are cocommutative in the category of symmetric spectra, orthogonal spectra, -spaces, -spaces and EKMM $\mathbb{…