# nLab setoid

## In higher category theory

#### Constructivism, Realizability, Computability

intuitionistic mathematics

# Setoids

## Idea

A setoid is a collection of things (which could be a set, a type, or a preset depending on the chosen foundations) equipped with an equivalence relation or a pseudo-equivalence relation. Setoids are commonly used in “impoverished” foundations of mathematics that lack a primitive notion of quotient; see for instance Bishop set.