A Layered Architecture for Universal Causality

of ﬁbration called a Grothendieck opﬁbration. We illustrate the UCLA architecture using a range of examples, including integer-valued multisets that represent a non-graphical framework for conditional independence, and causal models based on graphs and string diagrams using symmetric monoidal categories. We deﬁne causal effect in terms of the homotopy colimit of the nerve of the category of elements.