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(0,1)-category

(0,1)-topos

# Contents

## Definition

A $\sigma$-complete lattice is a lattice $(L, \leq, \bot, \vee, \top, \wedge)$ with a function

$\Vee_{n:\mathbb{N}} (-)(n): (\mathbb{N} \to L) \to L$

such that

• for all natural numbers $n \in \mathbb{N}$ and sequences $s: \mathbb{N} \to L$

$s(n) \leq \Vee_{n:\mathbb{N}} s(n)$
• for all elements $x \in L$ and sequences $s: \mathbb{N} \to L$ if $s(n) \leq x)$ for all natural numbers $n \in \mathbb{N}$, then

$\Vee_{n:\mathbb{N}} s(n) \leq x$