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most citedQuantum attacks on Bitcoin, and how to protect against them

225 citations

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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.CT2025

From clones to cm-monoids

Antonio Bucciarelli, Pierre-Louis Curien, Antonino Salibra

Clones of functions play a foundational role in both universal algebra and theoretical computer science. In this work, we introduce clone merge monoids (cm-monoids), a unifying one…

math.CT2024★ 1 cited

Correspondences between codensity and coupling-based liftings, a practical approach

Samuel Humeau, Daniela Petrisan, Jurriaan Rot

The Kantorovich distance is a widely used metric between probability distributions. The Kantorovich-Rubinstein duality states that it can be defined in two equivalent ways: as a su…

math.CT2024

Topoi with enough points and topological groupoids

Joshua Wrigley

We establish a bi-equivalence between the bi-category of topoi with enough points and a localisation of a bi-subcategory of topological groupoids

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.CT2023★ 1 cited

Towards a theory of natural directed paths

Philippe Gaucher

We introduce the abstract setting of presheaf category on a thick category of cubes. Precubical sets, symmetric transverse sets, symmetric precubical sets and the new category of (…