PlanetPhysics/C 3CategoryTheorem

\newcommand{\sqdiagram}[9]{Failed to parse (unknown function "\diagram"): {\displaystyle \diagram #1 \rto^{#2} \dto_{#4}& \eqno{\mbox{#9}}} }

\begin{theorem} ([[../Predicate/|proposition]] 1.2. in ref. .)

A cocomplete Abelian category is $C_3$ if and only if the direct limit of every direct family of subobjects $\left\{A_i\right\}$ of an [[../TrivialGroupoid/|object]] $A$ is equal to $\bigcup A_i$. \end{theorem}