# From Line Knowledge Digraphs to Sheaf Semantics: A Categorical Framework for Knowledge Graphs

arXiv: https://arxiv.org/abs/2603.05685 · HTML: https://mlsanity.com/paper/2603.05685/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2026.

## Built on by (most cited first, 1 of 1)

- [Toward Auto-Research: Mining Falsifiable Research Ideas from Paper Knowledge Graphs with Categorical Structure](https://mlsanity.com/paper/2608.20361/) (2026)

## Abstract (arXiv)

This paper proposes a categorical framework for knowledge graphs linking combinatorial graph structure with topos-theoretic semantics. Knowledge graphs are represented as labelled directed multigraphs and analysed through incidence matrices and line knowledge digraph constructions. The graph induces a free category whose morphisms correspond to relational paths. To model context-dependent meaning, a Grothendieck topology is defined on the free category generated by the graph leading to a topos of sheaves that supports local-to-global semantic reasoning. The framework connects graph-theoretic structure, categorical composition, and sheaf semantics in a unified mathematical model for contextual relational reasoning.