Linear quasi-categories as templicial modules

This is joint work with my supervisor Wendy Lowen. After laying out the basics of quasi-categories as defined by Joyal, we introduce a notion of linear quasi-categories over a unital commutative ring. We make use of certain colax monoidal functors, which we call templicial modules, as a variant of simplicial modules respecting the monoidal structure. It turns out that templicial modules with a Frobenius monoidal structure are equivalent to (homologically) non-negatively graded dg-categories. Through this equivalence we can associate to any dg-category a linear quasi-category, the linear dg-nerve, which enhances the classical dg-nerve.