Definition 4.17.
Let \(K\) be a congruence of small generation in a logos \(T\). We define the quotient of \(T\) by \(K\) as the localization
\[T/K \quad := \quad T[K^{-1}].\]
By Corollary 4.16, \(T/K\) is a logos and the localization map \(T \to T/K\) is a morphism of logoi.