F monoidal cats straightening

Remark 17.3.9. Using the straightening-unstraightening equivalence \(\Un ^{\cc }\colon \Fun (\Span _{L,R}(F), \Cat _{\infty }) \iso \Cocart (\Span _{L,R}(F))\), we may identify the category of \(\Ff \)-monoidal \(\infty \)-categories with a full subcategory of \(\Cocart (\Span _{L,R}(F))\). We denote the unstraightening of an \(\Ff \)-monoidal \(\infty \)-category \(C\) by \(p_{C}\colon C^{\otimes } \to \Span _{L,R}(F)\).