The framework of causal models provides a principled approach to causal
reasoning, applied today across many scientific domains. Here we present this
framework in the language of string diagrams, interpreted formally using
category theory. A class of string diagrams, called network diagrams, are in
1-to-1 correspondence with directed acyclic graphs. A causal model is given by
such a diagram with its components interpreted as stochastic maps, functions,
or general channels in a symmetric monoidal category with a 'copy-discard'
structure (cd-category), turning a model into a single mathematical object that
can be reasoned with intuitively and yet rigorously. Building on prior works by
Fong and Jacobs, Kissinger and Zanasi, as well as Fritz and Klingler, we
present diagrammatic definitions of causal models and functional causal models
in a cd-category, generalising causal Bayesian networks and structural causal
models, respectively. We formalise general interventions on a model, including
but beyond do-interventions, and present the natural notion of an open causal
model with inputs. We also give an approach to conditioning based on a
normalisation box, allowing for causal inference calculations to be done fully
diagrammatically. We define counterfactuals in this setup, and treat the
problems of the identifiability of causal effects and counterfactuals fully
diagrammatically. The benefits of such a presentation of causal models lie in
foundational questions in causal reasoning and in their clarificatory role and
pedagogical value. This work aims to be accessible to different communities,
from causal model practitioners to researchers in applied category theory, and
discusses many examples from the literature for illustration. Overall, we argue
and demonstrate that causal reasoning according to the causal model framework
is most naturally and intuitively done as diagrammatic reasoning.

本文引入了字符串图表语言解释的因果模型框架，并呈现了其在方向无环图的应用以及如何作为单个数学对象来思考。通过引入具有 “复制 - 丢弃” 结构的对称膜范畴 (cd - 范畴) 中的随机映射、函数或通道，我们将单纯因果模型的概念推广为基于网络图的因果模型和泛函因果模型的定义，并对一般干预、开放式因果模型进行了讨论及定义。同时，本文还定义了马尔可夫条件、逆因果与反事实关系等概念，并设计了一个基于归一化框的条件推断方法诠释因果效应与反事实关系的可辨认性问题。该研究具有广阔的应用领域和教育意义。