Category Theory Papers of the Week

To this end, we prove that, for every topological MV-algebra, the associated Mundici group can be endowed with a topology that extends the topology of the MV-algebra and makes it into an abelian topological $\ell$-group.

We prove the Díaz$\unicode[Arial]{x2013}$Park conjecture for sharpness of saturated fusion systems.

Our main result shows that, under the assumption of tautness, the same phenomenon holds at the categorified level, thereby offering a non-ultra-biased perspective on virtual ultracategories.

By introducing the notion of stable compatibility, we provide a framework in the model category theory which addresses the existence of a stable model structure on the category of modules over a monad.

We prove Lurie's proposed description of left rigid symmetric monoidal $(\infty,n)$-categories in terms of purely $\infty$-categorical data.

We prove that $\mathbf D^+_{\mathrm{fg},W}(R)=\operatorname{Loc}_{\mathrm{ex}}(\mathbf D^b_{\mathrm{fg},W}(R))$ whenever $W\subseteq\operatorname{Spec} R$ is specialization closed and has finite dimension.

For a quiver $Q$, we introduce and study $Q$-operads (or operads over $Q$), defined as a special sort of $\mathbf{fc}$-multicategories or virtual double categories, in which the directions of the arrows of $Q$ encode the permitted input orderings.

We construct an idempotent complete Frobenius exact category with an idempotent complete stable category in which a complete ideal cotorsion pair of object ideals induces a cotorsion pair of objects that fails to be complete.

We study how Koszul duality relates two kinds of boundary constructions associated with a smooth category and a proper category.

Three constructions of vertex operator algebras realizing the Haagerup center were announced independently and almost simultaneously. The relations between these constructions are studied in this paper.

We prove that every composition factor algebra is representation-finite.

This work broadens the synthetic applicability of promiscuous GDHs and provides a general strategy for engineering stereocomplementary biocatalysts for asymmetric synthesis.

This study demonstrates a general strategy for translating intricate molecular-recognition features into rational design principles, thereby facilitating the development of tailored biocatalysts for non-native substrates.

We study the representability of actions in varieties of algebras with $n \geq 1$ not necessarily associative bilinear multiplications.

In this paper, we formulate Land-Tamme's $\boxtimes$-construction and $\odot$-construction for continuous exact monads on dualizable stable $\infty$-categories, and establish the behaviour of localizing invariants on pushouts of left modules over continuous exact monads on dualizable stable $\infty$-categories.

It highlights sociology’s unique contribution in examining how ecological transformation is embedded in cultural values, social stratification, everyday practices, and spatial governance.

The goal of this paper is to provide lower and upper bounds on the ordinals that are needed to construct final coalgebras over $R$-modules as the limit of a transfinite sequence of functor iterations.

We study the structure of the category of representations of FA , the category of finite sets and all maps, working over a unital commutative ring.

We study the tensor triangular geometry of derived categories of valuation domains, obtaining complete ring-theoretic characterizations of their main structural properties.

We find bases for polynomial identities and calculate their codimensions for the Sweedler algebra, treating it first as an ordinary associative algebra over a field and second as a Hopf algebra.