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 andâ€¦ (More)

Wiring diagrams, as seen in digital circuits, can be nested hierarchically and thus have an aspect of self-similarity. We show that wiring diagrams form the morphisms of an operad T , capturing thisâ€¦ (More)

We give a new construction for rigidifying a quasi-category into a simplicial category, and prove that it is weakly equivalent to the rigidification given by Lurie. Our construction comes from theâ€¦ (More)

In this paper we present a simple database definition language: that of categories and functors. A database schema is a small category and an instance is a set-valued functor on it. We show thatâ€¦ (More)

We apply the Dwyer-Kan theory of homotopy function complexes in model categories to the study of mapping spaces in quasi-categories. Using this, together with our work on rigidification from [DS1],â€¦ (More)

We investigate the hierarchical structure of processes using the mathematical theory of operads. Information or material enters a given process as a stream of inputs, and the process converts it to aâ€¦ (More)

The category Man of smooth manifolds is not closed under arbitrary fiber products; for example the zeroset of a smooth function on a manifold is not necessarily a manifold, and the non-transverseâ€¦ (More)

In this paper we describe a functorial data migration [6] scenario about the manufacturing service capability of a distributed supply chain. The scenario is a category-theoretic analog of an OWLâ€¦ (More)

We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computerâ€¦ (More)