from this result even in the absence of such an assumption, we benefit from this accessory section to explain how to get rid of schemes which fail to be geometrically reduced, see Lemma \[25.10.2018–1\]. It is perhaps worth pointing out that it is at this point that additional properties of $A$—that it be Henselian and Japanese—start being required.

Recall that in Section \[04.07.2018–1\] we associated to a morphism ${\varphi}:Y\to X$ (satisfying certain assumptions) tensor categories ${\mathfrak{T}}_{\varphi}$ which, once polished, become neutral Tannakian ones. In Section \[FGS\] we put these categories together by employing the results of Section \[RFT\], this is made precise by Theorem \[05.11.2018–1\]. We are then able to construct a neutral Tannakian category ${\mathfrak{T}}_X$ which is a full subcategory of ${\mathbf{coh}}(X)$, see Definition \[30.10.2018–1\]. The group scheme associated to ${\mathfrak{T}}_X$ via the fibre functor $\bullet|_{x_0}:{\mathfrak{T}}_X\to{A\text{-}\mathbf{mod}}$, call it $\Pi(X,x_0)$, has the distinctive property that its category of representations ${{\mathrm{Rep}}_{A}(\Pi(X,x_0))}$ is equivalent to the full subcategory ${\mathfrak{T}}_X$ of ${\mathbf{coh}}(X)$. Under the assumption of normality, we are then able to show that $\Pi(X,x_0)$ is pro-quasi-finite (in the sense of Definition \[25.02.2019–1\]), see Theorem \[15.03.2019–1\]. If $A$ is in addition complete, the results of Section \[14.03.2019–1\] apply directly and we obtain that 