Item 2 (01DK) — The Clowder Project

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Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

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

We view the projection maps
\[ \webleft\{ \text{pr}_{i} \colon \prod _{i\in I}A_{i}\to A_{i}\webright\} _{i\in I} \]

as being given by

\[ \text{pr}_{i}\webleft (\webleft (a_{j}\webright )_{j\in I}\webright )\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}a_{i} \]

for each $\webleft (a_{j}\webright )_{j\in I}\in \prod _{i\in I}A_{i}$ and each $i\in I$.

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