Remark 1.1.5 ([Observation after Lemma 3.2., nLa26]).label Then using the usual encodings in set theory:

• The nullary cartesian product $\star$ is $\cali{P}(\emp)$

• The binary cartesian product $u\ti v$ is a subset of $\cali{P}(\cali{P}(u\cup v))$

• The general cartesian product $\prods{}{i\in I}u_{i}$ is a subset of $\cali{P}\parens{I\ti \cups{}{i\in I }u_i}$

• The nullary disjoint union is $\emp$

• The binary disjoint union $u\sqcup v$ is a subset of $2\ti (u\cup v)$

• The general disjoint union $\dcups{}{i\in I}u_{i}$ is a subset of $I\ti \cups{}{i\in I}u_{i}$

• The set of functions $u\to v$ is a subset of $\cali{P}(u\ti v)$