adj

• (not comparable, homological algebra, of a sequence of morphisms in an abelian category) Such that the kernel of each morphism is the image of the preceding one.
• (not comparable, homological algebra, of a functor of abelian categories) Such that it preserves short exact sequences.

verb

• (ambitransitive) To demand and enforce the payment or performance of, sometimes in a forcible or imperious way.
  "to exact tribute, fees, or obedience from someone"
• (transitive) To make desirable or necessary.
  "I vvait, Madam, / To knovv vvhat your commands are; my deſignes / Exact me in another place."
• (transitive) To inflict; to forcibly obtain or produce; to visit.
  "to exact revenge on someone"