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- W3023270957 abstract "We introduce a notion of enriched $infty$-categories over a suitable monoidal category, in analogy with quasi-categories over the category of sets. We make use of certain colax monoidal functors, which we call templicial objects, as a variant of simplicial objects respecting the monoidal structure. We relate the resulting enriched quasi-categories to nonassociative Frobenius monoidal functors, allowing us to prove that the free templicial module over an ordinary quasi-category is a linear quasi-category. To any dg-category we associate a linear quasi-category, the linear dg-nerve, which enhances the classical dg-nerve. Finally, we prove an equivalence between (homologically) non-negatively graded dg-categories on the one hand and templicial modules with a Frobenius structure on the other hand, indicating that nonassociative Frobenius templicial modules and linear quasi-categories can be seen as relaxations of dg-categories." @default.
- W3023270957 created "2020-05-13" @default.
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- W3023270957 creator A5049922117 @default.
- W3023270957 date "2020-05-10" @default.
- W3023270957 modified "2023-09-27" @default.
- W3023270957 title "Linear quasi-categories as templicial modules." @default.
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