In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be user-friendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global world-views. We finish by providing several different avenues for future research.

Abstract—Collaboration social networks are traditionally modeled using graphs that capture pairwise relationships but have ambiguity between group collaborations and multiple pairwise collaborations. We present a new approach to analyzing collaboration networks using simplicial complexes to represent the co-authorship collaborations. We formally define several key novel metrics: 1) higher dimensional analogs of vertex degree (e.g., simplex and facet degrees), 2) homology, and 3) minimal non-faces; and discuss their interpretation as it relates to coauthorship. We use these metrics in a study of an Army Research Lab dataset that includes the publications of the Communications & Networks Collaborative Technology Alliance. In particular, our study reveals many properties of large networks mirrored by this single-program publication dataset: the distinction of certain simplex degrees from vertex degrees, a power law characteristic in facet degrees, and some properties of topological “holes ” and minimal non-faces. I.