nLab topos of trees

Contents

Context

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

Contents

Definition

The topos of trees is the category of presheaves over the ordinal of natural numbers, ω\omega. More properly, this is the category of trees of height bounded by ω\omega, in that every path from the root has length ω\omega or less (when considered as ordinals). These trees can, however, be arbitrarily branching at every level.

An object is then a family of sets X iX_i for each iωi \in \omega with restriction functions X iX i+1X_i \leftarrow X_{i+1}. We can visualize this as a (potentially infinite) tree (really, forest) where an element of any X iX_i is a node of the tree, and the restriction functions map each node to its parent node.

Last revised on August 5, 2022 at 06:19:39. See the history of this page for a list of all contributions to it.