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416 papers in math.CT · page 1
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Directed univalence holds for simplicial objects in any ∞-topos
Directed univalence for simplicial objects in an $\infty$-topos
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Theory-topos duality defines conceptual completeness for logic fragments
Conceptual completeness for subgeometric logics
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Silting mutation extended to infinite dimensions
Large silting mutation in extriangulated categories
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Six functors prove ANR homology manifolds are cohomologically smooth
Homology manifolds via six functor formalisms
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Category theory structures AI identity as a hierarchy of criteria
A Category Theory Account of AI Identity
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Signed measures uniquely extend additive maps from positive measures
Signed Measures as the Linear Envelope of Positive Measures
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Marking generators invertible yields cofibrant ω-categories
Computads with invertible generators for weak {\omega}-categories
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Cartan subsemigroup yields Steinberg algebra via ultrafilter groupoid
Steinberg Algebras of Ample Semicategories and their Boolean-Cartan Restriction Semigroups
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Braided cogroupoids create monoidal equivalences on comodules
Braided cogroupoids
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Ideal n-cotorsion pairs match exactly in Frobenius categories and their stables
Ideal $n$-cotorsion pairs in Frobenius extriangulated categories
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Oriented polytopes present (∞,∞)-categories as sheaves
An Oriented Street--Roberts Conjecture
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Operad unifies gradient descent and wave equation
Compositional Dynamics in Learning and Mechanics
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Extensible doctrine morphisms coincide with ω-saturated ones
The points of canonical extensions of doctrines
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SFC-categories fix sober spaces as adjunction fixed points
A general framework for the faithful pointfree representation of $T_0$-spaces
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Quantum instruments compose by integrating channel-valued functions
Composing Quantum Instruments
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Quantum instrument monad generalizes state monad to quantum systems
The quantum instrument monad
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Factor graph recovery shrinks probabilistic CRNs while keeping inference fixed points
Reduction of Probabilistic Chemical Reaction Networks
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Lax grids let Gray tensor product arise by Day convolution
The Gray Product of $(\infty, n)$-Categories via Lax Grids
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Double-category monads are monadic over endomorphisms under colimit conditions
On categories of monads and comonads in double categories
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Isoregular theories yield accessible 2-categories with flexible limits
Isoregular theories, accessible 2-categories, and free constructions
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Semantics fixes the geometry of categorified spectra
Intrinsic Geometry of Categorified Spectral Objects
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Cleft extension restriction functors match on singular equivalences under equivariance
Equivariant Cleft Extensions and Singular Equivalences
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Framework transfers RL behavioral structures safely under abstraction
Compositional Behavioral Semantics for State Abstraction in Reinforcement Learning
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Silting properties ascend via left adjoints under explicit conditions
Migration of silting objects via adjoint pairs
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 is weakly equivalent to B haut(A)
On the Classifying Space of Homogeneous Functors
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Causal sufficiency defined by compatible Frobenius structures
Infinitesimal Causality
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Tannakian duality unifies etale
\'Etale Fundamental Groups -- a geometric and topological approach to fundamental groups in algebraic geometry
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Singularity category of triangular matrix equals lower block
Recollements of Triangulated Categories and the Singularity Category of a Triangular Matrix Category
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Virasoro c=1/2 module category equals Tambara-Yamagami over Z2
Conformal blocks, parenthesized braid operad, and $c=1/2$ Virasoro vertex operator algebra
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Codistinguished subcategories induce every exact structure
Codistinguished abelian subcategories
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Invariance under reformulation pins inference to the KL divergence
Reformulation Invariance and the Axiomatic Foundations of Inference
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Biased, unbiased and homotopy monoidal categories are equivalent
A (not so) short note: the equivalence of various notions of symmetric monoidal category
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Biased, unbiased and homotopy symmetric monoidal categories match
A (not so) short note: the equivalence of various notions of symmetric monoidal category
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Double simplicial objects produce spectral sequences in semi-abelian categories
Spectral Sequences in Semi-Abelian Categories
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Free internal frames constructed on presheaves of frames
Locales in presheaf toposes vs. presheaves of locales
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First example separates right from left integrality
Some Remarks About Integral Categories
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Cofibrant A-sets yield branching spaces independent of epsilon
Branching spaces of transverse sets
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Fiber bundles over categories reduce to constant fibers
Fiber bundles over small categories
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Nijenhuis Lie 2-algebras equivalent to 2-term Nijenhuis L∞-algebras
Nijenhuis Lie $2$-algebras
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Hopfological algebra gains a higher-categorical generalization
Hopfological algebra, revisited
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Monadic tensors embed neural symbols in unified truth semantics
NeSyCat Torch: A Differentiable Tensor Implementation of Categorical Semantics for Neurosymbolic Learning
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Categorical methods produce dual Amplituhedron
Brave new categorical spectral positive Schubert geometry and the categorical Dual Amplituhedron
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Complete axioms for probabilistic Boolean circuits as Markov kernels
Completeness for Probabilistic Boolean Tapes
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Trivial extensions create non-distributive lattices of thick tensor-ideals
Non-distributive lattices of thick tensor-ideals via trivial extensions
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Cross-connection semigroup equals finite-rank operator algebra
Cross-connections of the normed algebra of finite rank bounded operators on a Hilbert space
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Coextensions of monoid schemes form stacks of categorical groups
Deformation Theory of Monoid Schemes I
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Operads model LLM question decomposition as algebras
Operads for compositional reasoning in LLMs
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Poset isomorphisms link silting subcategories to s-torsion pairs
Silting subcategories and (co)torsion pairs associated to extended hearts
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Three monoidal structures force braidings to symmetries
A higher-order Eckmann-Hilton argument
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Relative dendroidal Rezk nerve ties to operad localization
Relative dendroidal Rezk nerve and applications