Ernst Althaus, Benjamin Merlin Bumpus, James Fairbanks, Emilio Minichiello, Daniel Rosiak A Parameterized Algorithm for Testing whether the Limit of a Diagram is Empty https://arxiv.org/abs/2605.24240

Kristopher Brown A Category-theoretic Reconstruction of Logical Expressivism https://arxiv.org/abs/2605.24796

Graham Manuell, Joshua L. Wrigley Generic bundles over a localic category https://arxiv.org/abs/2605.20407

Kevin D. Carlson, Ea E Thompson Exponentiable Virtual Double Categories and Representability of Exponentials https://arxiv.org/abs/2605.20586

Yorgo Chamoun Combinatorial manifolds and Kleene's theorem, homotopically https://arxiv.org/abs/2605.21142

Marco Grandis Enriched categories, real metrics and Lorentz manifolds https://arxiv.org/abs/2605.18088

Isaac Carcac\'ia-Campos, Enrique Mac\'ias-Virg\'os, David Mosquera-Lois Weak and Strong Fibrations of Functors https://arxiv.org/abs/2605.18650

Aaron David Fairbanks Monads in 2-categories https://arxiv.org/abs/2605.03102

Max Blans, Sil Linskens Free algebras via monoidal envelopes https://arxiv.org/abs/2605.03150

Keitaro Shiizuka Double coset for groupoids https://arxiv.org/abs/2605.03368

Keitaro Shiizuka Crossed Burnside rings for groupoids https://arxiv.org/abs/2605.03401

Nesta van der Schaaf Localic Relations with Open Cones https://arxiv.org/abs/2605.04038

Wei Hu, Ziheng Liu Metrics on triangulated categories and restrictions of (co)-$t$-structures https://arxiv.org/abs/2604.26199

Alejandro Fructuoso-Bonet, Jes\'us Rodr\'iguez-L\'opez Aggregation functions as lax morphisms of quantales https://arxiv.org/abs/2604.26775

Alexis Langlois-R\'emillard, Mateusz Stroi\'nski Diagrammatics for lax and Frobenius monoidal functors and weak morphism classifiers https://arxiv.org/abs/2604.24166

Benno Lossin Fibrations in Directed Type Theory https://arxiv.org/abs/2604.18668

Jean-Baptiste Vienney Extracting an $\mathbb{N}$-filtered differential modality from a differential modality https://arxiv.org/abs/2604.16016

Suddhasattwa Das Cells, convexity and contractibility in general categories https://arxiv.org/abs/2604.16126

Aubril Ony Internal structures in the category of right-preordered groups https://arxiv.org/abs/2604.14105

Matthew Collinson Topologically valued transition structures https://arxiv.org/abs/2604.14031

Christopher Doyle A Universal Quotient of Banking APIs https://arxiv.org/abs/2604.08833

Ois\'in Flynn-Connolly Enriched coalgebras are sometimes comonadic https://arxiv.org/abs/2604.09354

Quentin Karegar Baneh Kohal On the normal functor in the category of smooth vector bundles https://arxiv.org/abs/2604.07529

Paul Wilson Metacat: a categorical framework for formal systems https://arxiv.org/abs/2604.08331

Joe Moeller, Aaron D. Ames Hybrid Systems as Coalgebras: Lyapunov Morphisms for Zeno Stability https://arxiv.org/abs/2604.05255

Nao Mochizuki, Hiroyuki Nakaoka Higher exact dg-categories https://arxiv.org/abs/2604.05493

Yuto Kawase, Hayato Nasu On the decomposition of a strong epimorphism into regular epimorphisms https://arxiv.org/abs/2604.05744

Xiao-Wu Chen, Qiang Dong, Shiquan Ruan Frobenius quotients, inflation categories and weighted projective lines https://arxiv.org/abs/2604.02626

Shih-Yu Chang Categorified Spectral Sheaves and Homotopical Invariants for Noncommuting Operators https://arxiv.org/abs/2601.17597

Alexander Plakhotnikov Ricci flow as functor https://arxiv.org/abs/2601.17623

Jens Kosiol, Steffen Zschaler A note on nested conditions for finite categories of subgraphs https://arxiv.org/abs/2601.18376

K. Ganapathy, Sarang Sane Derived equivalences for complexes with support https://arxiv.org/abs/2601.16729

Max Demirdilek A lifting theorem for Grothendieck-Verdier categories https://arxiv.org/abs/2601.14812

Peng Xu Tensor Abelian geometry of VI-modules https://arxiv.org/abs/2601.14020

Roy Ferguson, Zurab Janelidze Partial Linearity in Categories https://arxiv.org/abs/2601.14237

Elena Caviglia, Zurab Janelidze, Luca Mesiti Comonadic approach to pretorsion theories https://arxiv.org/abs/2601.11472

Renaud Gauthier Consciousness in a Higher Categorical Context https://arxiv.org/abs/2601.06192

Steve Awodey, Joseph Hua Path Types in Algebraic Type Theory https://arxiv.org/abs/2601.06567

Enrico Pasqualetto, Timo Schultz, Janne Taipalus A categorical perspective on extended metric-topological spaces https://arxiv.org/abs/2601.07505

Khyathi Komalan Double Categorical Approaches to AQFT I: Axiomatic Setup https://arxiv.org/abs/2601.07807

Jiri Adamek Strongly finitary metric monads are too strong https://arxiv.org/abs/2601.03180

Dmytro Sukhov Tunnel Geometry and Proliferation Logic: A Strict Categorical Equivalence https://arxiv.org/abs/2601.00803

Sean Moss, Sam Staton A causal Markov category with Kolmogorov products https://arxiv.org/abs/2512.24417

Andrew Salch, Gunjeet Singh Notes on model structures on preorders https://arxiv.org/abs/2512.22518

Michael Batanin, Joachim Kock, Mark Weber Pita factorisation in operadic categories https://arxiv.org/abs/2512.22794

Masaki Fukuda, Tommy Shu 3-Crossed modules, Quasi-categories, and the Moore complex https://arxiv.org/abs/2512.22797

Takuo Matsuoka Notes on some categories related to that of finite totally ordered sets https://arxiv.org/abs/2512.22078

Josep Elgueta An alternative description of symmetric monoidal categories, and symmetric 2-groups https://arxiv.org/abs/2512.20717

Keegan J. Flood, Gabriele Lobbia, Giacomo Tendas Canonical differential calculi via functorial geometrization https://arxiv.org/abs/2512.20742

Florian Schwarz Differential bundles as functors from free modules https://arxiv.org/abs/2512.21147