Item 8 (00CW) — The Clowder Project

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

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

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

\[ \mathrm{coev}^{\odot }_{A,X}\webleft (a\webright )\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}[\mspace {-3mu}[x\mapsto a\odot x]\mspace {-3mu}] \]

for each $a\in A$.

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