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On (co)ends in \(\infty\)-categories. (English) Zbl 1470.18029
The principal objective in this paper is to lift the familiar equivalence of the definitions of (co)ends via twisted arrow categories \[ \mathrm{Tw}^{l}(\mathcal{C})\rightarrow\mathcal{C}^{\mathrm{op}}\times\mathcal{C} \] and via categories of simplices \[ \Delta_{/\mathcal{C}}\rightarrow\mathcal{C}^{\mathrm{op}}\times\mathcal{C} \] to \(\infty\)-caterories. It is also shown that weighted (co)limits, which can be defined as certain (co)ends, can altertively be described as (co)limits over left and right fibrations, respectively.

MSC:
18N60 \((\infty,1)\)-categories (quasi-categories, Segal spaces, etc.); \(\infty\)-topoi, stable \(\infty\)-categories
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
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