Definition:Left Exact Functor

Definition

Let $\mathbf A$ and $\mathbf B$ be categories.

Let $F : \mathbf A \to \mathbf B$ be a functor.

Then $F$ is left exact if and only if $F$ preserves finite limits.

Also See

• Definition:Right Exact Functor
• Definition:Exact Functor

Sources

• 2016: Emily Riehl: Category Theory in Context: Chapter $4$: Adjunctions $\S 4.5$: Adjunctions, limits, and colimits