A. Kaygun

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math.AT2026

Combinatorial Models for Linear Homotopy Theories

Atabey Kaygun

For a field $k$ of characteristic $0$ , we compare $k$ -linear chain complexes, semisimplicial vector spaces, augmented semisimplicial vector spaces, semicubical vector spaces, and a…

math.AT2026

Arboreal Objects and Their Homotopy Theory

Atabey Kaygun

We construct a category $\OrdFor$ as an arboreal extension of $I^_{epi} \subseteq I^$ , whose morphisms are ordered forests composed by grafting. We define a full functor $Ï…

math.AT2025

A Model Categoric Equivalence for Crossed Simplicial Modules

Haydar Can Kaya, Atabey Kaygun

We construct a model categorical equivalence between the category of simplicial vector spaces and the category of representations of a crossed simplicial group $I^ G$ when each $G_n…