The topos of trees is the category of presheaves over the ordinal of natural numbers, . More properly, this is the category of trees of height bounded by , in that every path from the root has length or less (when considered as ordinals). These trees can, however, be arbitrarily branching at every level.
An object is then a family of sets for each with restriction functions . We can visualize this as a (potentially infinite) tree (really, forest) where an element of any is a node of the tree, and the restriction functions map each node to its parent node.
Last revised on August 5, 2022 at 10:19:39. See the history of this page for a list of all contributions to it.