A graphical construction of free Markov categories
Yimu Yin
TL;DR
This paper introduces a graphical method for constructing free Markov categories using diagram surgeries, demonstrating functoriality over ordered directed acyclic graphs, which advances categorical probability theory.
Contribution
It presents a novel graphical construction technique for free Markov categories and establishes its functoriality, expanding the toolkit for categorical probability models.
Findings
Graphical surgery method for Markov categories
Functorial construction over DAGs
Enhanced understanding of categorical probability structures
Abstract
We describe how to perform surgeries on Joyal-Street style diagrams and thereby construct free Markov categories. We also show that the construction is functorial over ordered directed acyclic graphs.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models