Construction 5.80.
Given acyclic classes \(K\) and \(L\), we define
\[K \backslash L := \{\,f \mid K \ssquare f \subseteq L\,\}.\]
This is again an acyclic class by [Anel et al. 2025, Lemma 3.1.2 and Theorem 3.2.2]. If \(M\) is a third acyclic class, then we have
\[KM \subseteq L \iff M \subseteq K \backslash L,\]
so that \(K\backslash L\) functions as an internal hom in \(\Acyc(T)\).
References
- Mathieu Anel, Georg Biedermann, Eric Finster, André Joyal. Left-exact localizations of $\infty$-topoi III: The acyclic product. 2025.