Item 7 (00D8) — The Clowder Project

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Style 1	`book`	Alegreya Sans	`tcbthm`
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*To be replaced with Linus Romer's Elemaints when it is released.

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

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

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

for each $x\in X$.

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