Cokernel

Part of speech: noun

Definitions

1. In category theory, the quotient object obtained by identifying the image of a morphism with the codomain, representing the dual construction to a kernel
2. The categorical dual of a kernel, formed by taking the quotient of a target object by the equivalence relation induced by a morphism
3. A quotient construction in abstract algebra and category theory that is the counterpart to kernel, collapsing the codomain along the equivalence classes of a map

Etymology: "Cokernel" is a compound of "co-" and "kernel," built in English from parts that have been in the language for centuries. The "kernel" half descends from Old English "cyrnel," a diminutive formed from the Proto-Germanic word "kurnō," meaning grain or seed, and the same root gave English "corn" in its older sense of any cereal grain. A kernel is literally a small seed or the soft heart inside a shell or husk. The prefix "co-" comes from Latin "con-," meaning "with" or "together," and English has long used it to form words meaning shared or joint, such as "cooperate" and "coworker." Attaching it to "kernel" yields a sense of a kernel held in common with something else, a shared core of meaning or a joint nucleus.