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It is known that fuzzy set theory can be viewed as taking place within atopos. There are several equivalent ways to construct this topos, one is as thetopos of \'{e}tal\'{e} spaces over the topological space $Y=[0,1)$ with lowertopology. In this topos, the fuzzy subsets of a set $X$ are the subobjects ofthe constant \'{e}tal\'{e} $X\times Y$ where $X$ has the discrete topology.Here we show that the type-2 fuzzy truth value algebra is isomorphic to thecomplex algebra formed from the subobjects of the constant relational\'{e}tal\'{e} given by the type-1 fuzzy truth value algebra$\mathfrak{I}=([0,1],\wedge,\vee,\neg,0,1)$. More generally, we show that if$L$ is the lattice of open sets of a topological space $Y$ and $\mathfrak{X}$is a relational structure, then the convolution algebra $L^\mathfrak{X}$ isisomorphic to the complex algebra formed from the subobjects of the constantrelational \'{e}tal\'{e} given by $\mathfrak{X}$ in the topos of \'{e}tal\'{e}spaces over $Y$.

A topos view of the type-2 fuzzy truth value algebra