Acyclic Class

A class of morphisms $\mathcal{A}\subseteq\mathcal{E}^{\to}$ in a Logos $\mathcal{E}$ is an acyclic class if

• It is closed under composition
• Contains all Isomorphisms
• Is closed under Base Change
• Is closed under Colimits in the Arrow Category

Properties

• Every Congruence is an acyclic class.