Order is a fundamental mathematical structure. There are two natural ways to represent order structures, by posets and by causal-nets (acyclic directed graph). How can we compare these two ways, and which way would be more fundamental the other one?
To be more precise, I introduce causal-net category in https://arxiv.org/abs/2201.08963, whose objects are causal-nets and morphisms are functors between the path categories of causal-nets. This category is natural, but unlike the poset category, as far as I know, it is rarely studied. So I wonder if there are any natural connections between causal-net category and poset category?
