arXiv subjects

Daniel Fuentes-Keuthan

Publications and source records attributed to Daniel Fuentes-Keuthan.

3 recordsLinked to original sources

arXiv2020

Goodwillie Towers of $\infty$-Categories and Desuspension

We reconceptualize the process of forming $n$-excisive approximations to $\infty$-categories, in the sense of Heuts, as inverting the suspension functor lifted to $A_n$-cogroup objects. We characterize $n$-excisive $\infty$-categories as those $\infty$-categories in which $A_n$-cogroup objects admit desuspensions. Applying this result to pointed spaces we reprove a theorem of Klein-Schwänzl-Vogt: every 2-connected cogroup-like $A_\infty$-space admits a desuspension.

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arXiv2019

Modelling Connective Spectra via Multicategories

We put a model structure on a full subcategory of based multicategories in which the weak equivalences are created by the K-theory functor of Elmendorf-Mandell, providing a model categorical lift of Thomason's theorem on the modeling of connective spectra by symmetric monoidal categories. We note that this lifts to a semi-modelstructure on based multicategories itself. As a corollary we show that to model connective spectra up to stable equivalence it suffices to restrict to symmetric monoidal groupoids.

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arXiv2018

A model structure on prederivators for $(\infty,1)$-categories

By theorems of Carlson and Renaudin, the theory of $(\infty,1)$-categories embeds in that of prederivators. The purpose of this paper is to give a two-fold answer to the inverse problem: understanding which prederivators model $(\infty,1)$-categories, either strictly or in a homotopical sense. First, we characterize which prederivators arise on the nose as prederivators associated to quasicategories. Next, we put a model structure on the category of prederivators and strict natural transformations, and prove a Quillen equivalence with the Joyal model structure for quasicategories.

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