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math.CT2025
The free bifibration on a functor
Bryce Clarke, Gabriel Scherer, Noam Zeilberger
We consider the problem of constructing the free bifibration generated by a functor of categories . This problem was previously considered by Lamarche, and is closely…
math.CT2024★ 1 cited
The categorical contours of the Chomsky-Schützenberger representation theorem
Paul-André Melliès, Noam Zeilberger
We develop fibrational perspectives on context-free grammars and on nondeterministic finite-state automata over categories and operads. A generalized CFG is a functor from a free c…
math.CT2022★ 3 cited
Parsing as a lifting problem and the Chomsky-Schützenberger representation theorem
Paul-André Melliès, Noam Zeilberger
We begin by explaining how any context-free grammar encodes a functor of operads from a freely generated operad into a certain "operad of spliced words". This motivates a more gene…