Item 3 (00RN) — The Clowder Project

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`

Interaction With Identities. For each $A\in \text{Obj}\webleft (\mathsf{Sets}\webright )$, we have ^[1]
\[ \webleft (\chi _{A}\webright )_{*}=\text{id}_{\mathcal{P}\webleft (A\webright )}. \]

Footnotes

[1] That is, the postcomposition function

\[ \webleft (\chi _{A}\webright )_{*}\colon \mathrm{Rel}\webleft (\text{pt},A\webright )\to \mathrm{Rel}\webleft (\text{pt},A\webright ) \]

is equal to $\text{id}_{\mathrm{Rel}\webleft (\text{pt},A\webright )}$.

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