ScalingStacks

Notation 5.1.8.

Let \(\alpha \colon \partial c_k \rightarrow\mathcal C\) be a pair of parallel \((k-1)\)-morphisms in an \((\infty,k)\)-category \(\mathcal C\). The space of \(k\)-morphisms filling \(\alpha\) is \[\mathrm{kHom}_{\mathcal C}(\alpha) \coloneqq \mathrm{Hom}_{\mathrm{Cat}_{(\infty, {k})}}(c_k, \mathcal C) \times_{\mathrm{Hom}_{\mathrm{Cat}_{(\infty, {k})}}(\partial c_k, \mathcal C)} \{\alpha\}.\]