Related papers: The core of adjoint functors

We compare derived categories of the category of strict polynomial functors over a finite field and the category of ordinary endofunctors on the category of vector spaces. We introduce two intermediate categories: the category of…

We study the polytopes of affine maps between two polytopes -- the hom-polytopes. The hom-polytope functor has a left adjoint -- tensor product polytopes. The analogy with the category of vector spaces is limited, as we illustrate by a…

Polynomial functors are a categorical generalization of the usual notion of polynomial, which has found many applications in higher categories and type theory: those are generated by polynomials consisting a set of monomials built from sets…

Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract…

We show that the category of corings over a fixed base ring with local units is equivalent to the category of comonads in (right) unital modules whose underlying functors preserve inductive limits. Changing base rings, we prove a…

If a Quillen model category can be specified using a certain logical syntax (intuitively, ``is algebraic/combinatorial enough''), so that it can be defined in any category of sheaves, then the satisfaction of Quillen's axioms over any site…

In this paper we {\em discuss} diverse aspects of mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize on the behaviour of row and column operators as they turn out to be…

A theorem that is of aid in computing the domain of the adjoint operator is provided. It may serve e.g. as a criterion for selfadjointness of a symmetric operator, for normality of a formally normal operator or for $H$--selfadjointness of…

An (additive) functor F from an additive category A to an additive category B is said to be objective, provided any morphism f in A with F(f) = 0 factors through an object K with F(K) = 0. In this paper we concentrate on triangle functors…

In this paper we define a functor-- leveled sub-cohomology. (It bears no relation with the level of elliptic curves). It is based on leveled cycles on a smooth projective variety, and will be expected to reveal a structure in the level.

In this paper we develop the theory of topological categories over a base category, that is, a theory of topological functors. Our notion of topological functor is similar to (but not the same) the existing notions in the literature (see…

For a given family $\{(\mathrm{q}_i, \mathrm{t}_i, \mathrm{p_i} )\}_{i \in I}$ of adjoint triples between exact categories $\mathcal{C}$ or $\mathcal{D}$, we show that any cotorsion pair in $\mathcal{C}$ and $\mathcal{D}$ yield two…

We introduce an exact functor defined on multigraded modules which we call the expansion functor and study its homological properties. The expansion functor applied to a monomial ideal amounts to substitute the variables by monomial prime…

Let $R$ be a commutative local ring. We study the subcategory of the homotopy category of $R$-complexes consisting of the totally acyclic $R$-complexes. In particular, in the context where $Q\to R$ is a surjective local ring homomorphism…

This note aims to introduce a left adjoint functor to the functor which assigns a heap to a group. The adjunction is monadic. It is explained how one can decompose a free group functor through the previously introduced adjoint and employ it…

For any 0-cell $B$ in a 2-category $\Bc$ we introduce the notion of adjoint algebra $\adj_B$. This is an algebra in the center of $\Bc$. We prove that, if $\ca$ is a finite tensor category, this notion applied to the 2-category of…

We study polynomial functors in the incompressible category $\text{Ver}_4^+$, which can be viewed as super polynomial functors in characteristic 2. Concretely, we classify additive, exact and simple polynomial functors, and describe how…

We introduce the notion of numerical functors to generalise Eilenberg & MacLane's polynomial functors to modules over a binomial base ring. After shewing how these functors are encoded by modules over a certain ring, we record a precise…

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…

We show that the left and right adjoint of the Schur functor can be expressed in terms of the monoidal structure of strict polynomial functors. Using this result we give a necessary and sufficient condition for when the tensor product of…