Item 7 (00CV) — The Clowder Project

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*To be replaced with Linus Romer's Elemaints when it is released.

The Tensor Evaluation Map. For each $X,Y\in \text{Obj}\webleft (\mathsf{Sets}_{*}\webright )$, we have a map
\[ \mathrm{ev}^{\odot }_{X,Y}\colon \mathsf{Sets}_{*}\webleft (X,Y\webright )\odot X\to Y, \]

natural in $X,Y\in \text{Obj}\webleft (\mathsf{Sets}_{*}\webright )$, and given by

\[ \mathrm{ev}^{\odot }_{X,Y}\webleft (f\odot x\webright )\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}f\webleft (x\webright ) \]

for each $f\odot x\in \mathsf{Sets}_{*}\webleft (X,Y\webright )\odot X$.

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