Boolean local topos

A Boolean local topos is a specific type of mathematical structure named after George Boole, who developed Boolean algebra. This algebra is a system of mathematical logic that represents relationships between ideas or objects, forming the basis for electronic digital computers.1

In the context of topos theory, a Boolean topos is one where its internal language is considered "classical." A Boolean topos is "local" under certain conditions, meaning that for any statement p, either p is true or its negation ¬p is true. This property is related to the disjunction property and the existence property, which, when combined with De Morgan's laws, simplify the description of a Boolean local topos. Essentially, it's a topos where if two functions are identical for all inputs from a specific object, then the functions themselves are identical.2