相关论文: Exponentiable functors between quantaloid-enriched…
We present a logical and algebraic description of right adjoint functors between generalized quasi-varieties, inspired by the work of McKenzie on category equivalence. This result is achieved by developing a correspondence between the…
Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers-Loeser in the context of semi-algebraic and sub-analytic structures, when they studied stability under…
We use the abstract setting of excisive functors in the language of $\infty$-categories to show that the best approximation to the $\ell^1$-homology functor by an excisive functor is trivial. Then we make an effort to explain the used…
Partial difference operators for a large class of functors between presheaf categories are introduced, extending our difference operator from \cite{Par24} to the multivariable case. These combine into the Jacobian profunctor which provides…
We prove existence of equalizers in certain categories of cocomplete cocategories. This allows us to complete the proof of the fact that A-infinity functor categories arise as internal Hom-objects in the category of differential graded…
A folklore result in category theory is that a (weakly) Cartesian closed category with finite co-products is distributive. Usually, the proof of this small result is carried on using the fact that the exponential functor is right adjoint to…
We give a sufficient condition for an Ext-finite triangulated category to be saturated. Saturatedness means that every contravariant cohomological functor of finite type to vector spaces is representable. The condition consists in existence…
The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext…
We define the notion of an additive model category, and we prove that any additive, stable, combinatorial model category has a natural enrichment over symmetric spectra based on simplicial abelian groups. As a consequence, every object in…
Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This…
We show under suitable finiteness conditions that a functor between abelian categories induces a (not necessarily additive) map between their Grothendieck groups. This is related to the derived functors of Dold and Puppe, and generalizes a…
We develop a theory of weighted colimits in the framework of weakly bienriched $\infty$-categories, an extension of Lurie's notion of enriched $\infty$-categories. We prove an existence result for weighted colimits, study weighted colimits…
We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some…
A classification is provided of functors, in particular polynomial ones, from a category with a zero object in which every object is a finite sum of copies of a generating object, into an abelian category. This classification is extended to…
We extend Lurie's definition of enriched $\infty$-categories to notions of left enriched, right enriched and bienriched $\infty$-categories, which generalize the concepts of closed left tensored, right tensored and bitensored…
We extend the notion of exact completion on a weakly lex category to elementary doctrines. We show how any such doctrine admits an elementary quotient completion, which freely adds effective quotients and extensional equality. We note that…
We define Euler characteristic of a category enriched by a monoidal model category. If a monoidal model category V is equipped with Euler characteristic that is compatible with weak equivalences and fibrations in V, then our Euler…
We introduce a new categorical framework for studying derived functors, and in particular for comparing composites of left and right derived functors. Our central observation is that model categories are the objects of a double category…
The well-known difficulties arising in a classification which is not set-theoretically trivial---involving what is sometimes called a non-smooth quotient---have been overcome in a striking way in the theory of operator algebras by the use…
We give an elementary characterization of those quantaloids Q for which the category Cat(Q) of Q-enriched categories and functors is cartesian closed. We then unify several known cases (previously proven using ad hoc methods) and we give…