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In 1997, Hofmann and Streicher introduced an explicit construction to lift a Grothendieck universe from the category of sets into the category of set-valued presheaves on a small category. More recently, Awodey presented an elegant…

Category Theory · Mathematics 2026-04-29 Andrew Slattery , Jonathan Sterling

We present a new coherence theorem for comprehension categories, providing strict models of dependent type theory with all standard constructors, including dependent products, dependent sums, identity types, and other inductive types.…

Logic · Mathematics 2016-04-20 Peter LeFanu Lumsdaine , Michael A. Warren

We construct a cofibrantly generated model structure on the category of flows such that any flow is fibrant and such that two cofibrant flows are homotopy equivalent for this model structure if and only if they are S-homotopy equivalent.…

Algebraic Topology · Mathematics 2021-08-24 Philippe Gaucher

We show that under certain conditions, well-studied algebraic properties transfer from the class $\mathcal{Q}_{_\text{RFSI}}$ of the relatively finitely subdirectly irreducible members of a quasivariety $\mathcal{Q}$ to the whole…

Logic · Mathematics 2023-06-06 Wesley Fussner , George Metcalfe

An old theorem of Ad\'amek constructs initial algebras for sufficiently cocontinuous endofunctors via transfinite iteration over ordinals in classical set theory. We prove a new version that works in constructive logic, using "inflationary"…

Logic · Mathematics 2022-11-04 Andrew M. Pitts , S. C. Steenkamp

In the paper "Cotorsion Pairs in C(R-Mod)", the authors construct an abelian model structure on the category of chain complexes Ch(R), where the class of cofibrant objects is given by the class of degreewise projective chain complexes.…

Category Theory · Mathematics 2012-07-03 Marco Pérez

Part 2 of 3 from master's thesis: Modeling Compact Objects with Effective Field Theory. Using the Effective Field Theory framework for extended objects, we build the effective theory of a binary system made up of the most general compact…

High Energy Physics - Theory · Physics 2023-04-06 Irvin Martinez

Manifold learning and effective model building are generally viewed as fundamentally different types of procedure. After all, in one we build a simplified model of the data, in the other, we construct a simplified model of the another…

History and Philosophy of Physics · Physics 2024-11-26 David Peter Wallis Freeborn

We construct a category $\OrdFor$ as an arboreal extension of $\Delta_{\mathrm{epi}}\subseteq\Delta$, whose morphisms are ordered forests composed by grafting. We define a full functor $\pi\colon \OrdFor\to\Delta_{\mathrm{epi}}^{op}$…

Algebraic Topology · Mathematics 2026-04-03 Atabey Kaygun

The simplicial extension of any functor from Sets to Sets which commutes with directed colimits takes weak equivalences to weak equivalences. The goal of the present paper is construct a framework which can be used to proof results of this…

Algebraic Geometry · Mathematics 2009-09-28 Vladimir Voevodsky

We generalise the usual notion of fibred category; first to fibred 2-categories and then to fibred bicategories. Fibred 2-categories correspond to 2-functors from a 2-category into 2-Cat. Fibred bicategories correspond to trihomomorphisms…

Category Theory · Mathematics 2013-03-26 Mitchell Buckley

We construct a model structure on the category $\mathrm{DblCat}$ of double categories and double functors, whose trivial fibrations are the double functors that are surjective on objects, full on horizontal and vertical morphisms, and fully…

Algebraic Topology · Mathematics 2023-06-21 Lyne Moser , Maru Sarazola , Paula Verdugo

It is well-known in universal algebra that adding structure and equational axioms generates forgetful functors between varieties, and such functors all have left adjoints. The category of elementary doctrines provides a natural framework…

Category Theory · Mathematics 2024-05-14 Francesca Guffanti

We provide bar and cobar constructions as functors acting between various categories of curved operads and curved cooperads. Cobar and bar constructions are adjoint to each other. Given a twisting cochain between a curved augmented cooperad…

K-Theory and Homology · Mathematics 2014-03-17 Volodymyr Lyubashenko

By using the Dold-Kan correspondence we construct a Quillen adjunction between the model categories of non-cocommutative coassociative simplicial and differential graded coalgebras over a field. We restrict to categories of connected…

Category Theory · Mathematics 2015-06-02 Hermann Soré

This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways…

Logic in Computer Science · Computer Science 2016-11-14 Cyril Cohen , Thierry Coquand , Simon Huber , Anders Mörtberg

We introduce the notion of an enriched fibration, i.e. a fibration whose total category and base category are enriched in those of a monoidal fibration in an appropriate way. Furthermore, we provide a way to obtain such a structure,…

Category Theory · Mathematics 2018-07-09 Christina Vasilakopoulou

Lucatelli Nunes obtained a 2-categorical version of the adjoint triangle theorem of Dubuc using the descent object of a specific diagram. In some cases, such a diagram can be filled with an extra cell. We show then how to obtain a biadjoint…

Category Theory · Mathematics 2025-03-14 Gabriel Merlin

The contributions of this paper are twofold. Within the framework of Grothendieck's fibrational category theory, we present a web of fundamental 2-adjunctions surrounding the formation of the category of all small diagrams in a given…

Category Theory · Mathematics 2021-03-09 George Peschke , Walter Tholen

We initiate in this article the study of weakly exact structures, a generalization of Quillen exact structures. We introduce weak counterparts of one-sided exact structures and show that a left and a right weakly exact structure generate a…

Category Theory · Mathematics 2023-07-19 Rose-Line Baillargeon , Thomas Brüstle , Mikhail Gorsky , Souheila Hassoun