Lili Shen

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math.CT2025

Cartesian closedness of the category of real-valued sets, I

Lili Shen, Jian Zhang

Let $[0, 1]_{*}$ be the unit interval $[0, 1]$ equipped with a continuous t-norm $*$ . It is shown that the category of $[0, 1]_{*}$ -sets is cartesian closed if, and only if, $*$ is the mi…

math.CT2025

$Q - Set$ is not generally a topos

Xiao Hu, Lili Shen

For a commutative, unital and divisible quantale $Q$ , it is shown that the category of $Q$ -sets is a topos if, and only if, $Q$ is a frame.

Cartesian closedness of the category of real-valued sets, I

Q-Set is not generally a topos

$Q - Set$ is not generally a topos