ScalingStacks

Unpacked, a centralizer is an object \(\mathfrak{Z}(f) \in \mathcal C\) equipped with morphisms \(u \colon I \rightarrow\mathfrak{Z}(f)\) and \(\mathrm{ev}\colon \mathfrak{Z}(f) \otimes A \rightarrow B\), such that the following diagram commutes and which is final among such pairs: for any pair of morphisms \(u_X\colon I \rightarrow X\) in \(\mathcal C\) and \(\mathrm{ev}_X\colon X\otimes A \rightarrow B\) making the analog of ([00EM]) commute, there is a unique morphism \(\varphi\colon X \rightarrow\mathfrak{Z}(f)\) such that commutes.