ScalingStacks

Definition 1.1. Let $ℱ$ be a full subcategory of a category $𝒞$ and suppose $X$ is an object of $𝒞$. A morphism $\varphi :X\to F$ with $F\in ℱ$ is called an $ℱ$-preenvelope if for each morphism $X\to F^{\prime }$ with $F^{\prime }\in ℱ$ there exists a morphism $F\to F^{\prime }$ making the following triangle commute.