2016/12/08 by Yonatan Harpaz, Harpaz, Yonatan, Joost Nuiten +3 · 1 citation
Mathematics · Medicine · #18D50 #18G55 #55P42 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Pituitary Gland Disorders and Treatments
paper · pdf · doi:10.48550/arxiv.1612.02607
openalex publication_date 2016/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Associated to a presentable ∞-category C and an object X ∈ C is the tangent ∞-category TXC, consisting of parameterized spectrum objects over X. This gives rise to a cohomology theory, called Quillen cohomology, whose category of coefficients is TXC. When C consists of algebras over a nice ∞-operad in a stable ∞-category, TXC is equivalent to the ∞-category of operadic modules, by work of Basterra--Mandell, Schwede and Lurie. In this paper we develop the model-categorical counterpart of this identification and extend it to the case of algebras over an enriched operad, taking values in a model category which is not necessarily stable. This extended comparison can be used, for example, to identify the cotangent complex of enriched categories, an application we take up in a subsequent paper.