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.
Read more about this topic: Limit (category Theory)
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