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math.CT2024
2-Rig Extensions and the Splitting Principle
John C. Baez, Joe Moeller, Todd Trimble
Classically, the splitting principle says how to pull back a vector bundle in such a way that it splits into line bundles and the pullback map induces an injection on -theory. H…
math.CT2021
The Grothendieck Construction in Categorical Network Theory
Joe Moeller
In this thesis, we present a flexible framework for specifying and constructing operads which are suited to reasoning about network construction. The data used to present these ope…
math.CT2018
Noncommutative Network Models
Joe Moeller
Network models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of netwo…