Characterizations of Left and Right Exactness in Abelian Categories

category-theory
Author

sun123zxy

Published

October 11, 2026

colim I ⊣ ∆ ⊣ lim I leftadjoint rightadjoint preservescolimits preserveslimits preservefnitecolimits preservefnitelimits preservecokernels preservekernels rightexact leftexact exact assumptions: abeliancategoryadditivefunctor small(co)limits colim I is lim I is + I fltered/discrete+ R Mod (AB5)colim I is + I discrete+ R Mod (AB4*)lim I is + perservedirectsums + preservedirectproducts
Figure 1