A weak multilimit is a common generalization of multilimits and weak limits.
If is a diagram in a category , then a weak multilimit of is a (small) set of cones over such that any other cone over factors (not necessarily uniquely) through some (not necessarily unique) element of . If the factorization, and the cone factored through, are unique, then is a multilimit, whereas if is a singleton, then it is a weak limit.
The existence of weak multilimits is a “pure size condition” on , in the sense that if is a small category, then every small diagram in (that is, every functor where is also small) has a weak multilimit, namely the set of all cones over .
Of course, weak multilimits in are called weak multicolimits in .
Last revised on February 1, 2010 at 17:03:05. See the history of this page for a list of all contributions to it.