Causal trees represented by Darondeau and Degano are one of the truly concurrent model for distributed systems and processes. The model is more basic than other truly concurrent models because it defines concurrency and causality with respect to a branch, but on the other hand it is more expressive than the latter because its possible runs can be freely specified in terms of a tree.

The intention of the paper is to connect two distinct approaches to which the category theory has been applied in order to investigate causal trees and their timed extensions. In particular, we establish that in the case of causal trees, the approaches are equivalent, but it is not true in the case of timed causal trees.

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