A thread is an element of a cofiltered limit of topological spaces (usually studied in the generality of projective spectra?) or (in a more rarely used terminology) of a cofiltered limit of sets.
Thus let be a functor where is a smallfiltered category (for example, a directed set). Then consists of families where and for every morphism in , . Such families are called threads.
If is a functor where is a small filtered category then has the same underlying set (of threads) as the composition where is the forgetful functor; the topology of is the subspace topology on understood as a subset of the Cartesian product equipped with the (product)Tihonov's topology.
Revised on May 11, 2012 04:38:18
by Toby Bartels