CatDat

Implication Details

Assumptions: finite powers, sequential limits

Conclusions: countable powers

Proof: We can write $X^{\IN}$ as the limit of the sequence $\cdots \to X^3 \to X^2 \to X \to 1$ with transition morphisms $f_n : X^{n+1} \to X^n$, $(x_1,\dotsc,x_{n+1}) \mapsto (x_1,\dotsc,x_n)$, i.e., $p_i f_n = p_i$ for $1 \leq i \leq n$.