Limit (category Theory) - A Note On Terminology

A Note On Terminology

Older terminology referred to limits as "inverse limits" or "projective limits," and to colimits as "direct limits" or "inductive limits." This has been the source of a lot of confusion.

There are several ways to remember the modern terminology. First of all,

• cokernels,
• coequalizers, and
• codomains

are types of colimits, whereas

• kernels,
• equalizers, and
• domains

are types of limits. Second, the prefix "co" implies "first variable of the ". Terms like "cohomology" and "cofibration" all have a slightly stronger association with the first variable, i.e., the contravariant variable, of the bifunctor.