Abstract
Associated to a presentable infinity-category nd an object X is an element of C is the tangent infinity-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 consists of algebras over a nice infinity-operad in a stable infinity-category, is equivalent to the ...
Abstract
Associated to a presentable infinity-category nd an object X is an element of C is the tangent infinity-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 consists of algebras over a nice infinity-operad in a stable infinity-category, is equivalent to the infinity-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.
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