Sergei O. Ivanov

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math.AT2026

The discrete homotopy hypothesis for directed graphs

Briony Eldridge, Sergei O. Ivanov, Xiaomeng Xu +2

We develop a homotopy theory of directed graphs based on cubical homotopy groups, also known as $A$ -groups or reduced GLMY homotopy groups. Localizing the category of directed grap…

math.AT2025

Bousfield-Kan completion as a codensity $\infty$ -monad

Emmanuel Dror Farjoun, Sergei O. Ivanov

Working in the setting of $\infty$ -categories, we develop a general theory of the codensity monad $T_{D}$ associated with a full subcategory $\mathcal{D}\subseteq \mathcal{…

The discrete homotopy hypothesis for directed graphs

Bousfield-Kan completion as a codensity ∞-monad

Bousfield-Kan completion as a codensity $\infty$ -monad