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A survey of properties of the adjunction involving a semisymmetrization functor, which was suggested by J.D.H. Smith, and which maps the category of quasigroups with homotopies to the category of semisymmetric quasigroups with…

Category Theory · Mathematics 2016-01-13 Aleksandar Krapez , Zoran Petric

We prove that a Quillen adjunction of model categories (of which we do not require functorial factorizations and of which we only require finite bicompleteness) induces a canonical adjunction of underlying quasicategories.

Category Theory · Mathematics 2015-01-14 Aaron Mazel-Gee

The aim of this paper is to establish a contravariant adjunction between the category of quasi-bialgebras and a suitable full subcategory of dual quasi-bialgebras, adapting the notion of finite dual to this framework. Various functorial…

Quantum Algebra · Mathematics 2019-05-29 Alessandro Ardizzoni , Laiachi El Kaoutit , Paolo Saracco

We prove the theorem stated in the title. More precisely, we show the stronger statement that every symmetric monoidal left adjoint functor between presentably symmetric monoidal infinity-categories is represented by a strong symmetric…

Algebraic Topology · Mathematics 2017-10-03 Thomas Nikolaus , Steffen Sagave

The notion of quasicrossed product is introduced in the setting of G-graded quasialgebras, i.e., algebras endowed with a grading by a group G, satisfying a "quasiassociative" law. The equivalence between quasicrossed products and…

Rings and Algebras · Mathematics 2014-12-01 Helena Albuquerque , Elisabete Barreiro , José M. Sánchez-Delgado

We prove a variant of Emerton's conjecture concerning the right derived functors of the ordinary parts functor $\operatorname{Ord}_P^G$. This functor plays an important role in the theory of mod $p$ representations of $p$-adic reductive…

Representation Theory · Mathematics 2025-08-21 Manuel Hoff , Sarah Diana Meier , Michael Spieß , Claudius Heyer

Let $R$ be an associative ring with unit. This paper deals with various aspects of the category of functors of $\mathcal R$-modules; that is, the category of additive and covariant functors from the category of R-modules to the category of…

Category Theory · Mathematics 2019-04-01 Adrián Gordillo , José Navarro , Pedro Sancho

In this paper we investigate the categories of braided objects, algebras and bialgebras in a given monoidal category, some pairs of adjoint functors between them and their relations. In particular we construct a braided primitive functor…

Category Theory · Mathematics 2013-04-15 Alessandro Ardizzoni , Claudia Menini

We develop a 2-dimensional version of accessibility and presentability compatible with the formalism of flat pseudofunctors. First we give prerequisites on the different notions of 2-dimensional colimits, filteredness and cofinality; in…

Category Theory · Mathematics 2025-08-05 Ivan Di Liberti , Axel Osmond

We investigate notions of support and cosupport for differential graded (DG) modules over DG algebras. We apply these notions to identify certain classes of derived functors that are able to detect triviality and isomorphisms in derived…

Commutative Algebra · Mathematics 2021-11-30 Keri Sather-Wagstaff

We prove that the derived parabolic induction functor, defined on the unbounded derived category of smooth mod $p$ representations of a $p$-adic reductive group, admits a left adjoint $\mathrm{L}(U,-)$. We study the cohomology functors…

Representation Theory · Mathematics 2024-01-19 Claudius Heyer

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 show that the quasiequational theory of a relatively congruence modular quasivariety of left $R$-modules is determined by a two-sided ideal in $R$ together with a filter of left ideals. The two-sided ideal encodes the identities that…

Rings and Algebras · Mathematics 2015-09-15 Keith A. Kearnes

In a previous paper we introduced the concept of semiseparable functor. Here we continue our study of these functors in connection with idempotent (Cauchy) completion. To this aim, we introduce and investigate the notions of (co)reflection…

Category Theory · Mathematics 2023-06-13 Alessandro Ardizzoni , Lucrezia Bottegoni

We investigate the connection between left exact $\infty$-functors between finitely complete quasicategories and exact functors between fibration categories, describing a procedure to approximate flat $\infty$-functors of the former type by…

Category Theory · Mathematics 2026-02-20 El Mehdi Cherradi

We introduce the notion of a quasi DG category, generalizing that of a DG category. To a quasi DG category satisfying certain additional conditions, we associate another quasi DG category, the quasi DG category of $C$-diagrams. We then show…

Algebraic Geometry · Mathematics 2014-01-03 Masaki Hanamura

We construct an "almost involution" assigning a new DG-category to a given one, and use this construction to recover, say, the abelian category of graded modules over the graded ring $R^*$ from the DG-category of DG-modules over a DG-ring…

Category Theory · Mathematics 2025-10-08 Leonid Positselski

A function in a class $\mathcal{F}(X)$ is said to be subdifferentially determined in $\mathcal{F}(X)$ if it is equal up to an additive constant to any function in $\mathcal{F}(X)$ with the same subdifferential. A function is said to be…

Optimization and Control · Mathematics 2018-10-16 Marc Lassonde

The bicategory of Landau-Ginzburg models denoted by LGK possesses adjoints and this helps in explaining a certain duality that exists in the setting of Landau-Ginzburg models in terms of some specified relations. The construction of LGK is…

Category Theory · Mathematics 2024-02-05 Yves Baudelaire Fomatati

For an associative ring $R$, let $P$ be an $R$-module with $S=\End_R(P)$. C.\ Menini and A. Orsatti posed the question of when the related functor $\Hom_R(P,-)$ (with left adjoint $P\ot_S-$) induces an equivalence between a subcategory of…

Category Theory · Mathematics 2009-09-18 John Clark , Robert Wisbauer