Related papers: Bicategories of spans as generic bicategories
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Given a 2-category $\twocat{K}$ admitting a calculus of bimodules, and a 2-monad T on it compatible with such calculus, we construct a 2-category $\twocat{L}$ with a 2-monad S on it such that: (1)S has the adjoint-pseudo-algebra property.…
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Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades,…
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In previous work by the first two authors, Frobenius and commutative algebra objects in the category of spans of sets were characterized in terms of simplicial sets satisfying certain properties. In this paper, we find a similar…
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We prove an ambidexterity result for $\infty$-categories of $\infty$-categories admitting a collection of colimits. This unifies and extends two known phenomena: the identification of limits and colimits of presentable $\infty$-categories…
We prove a universal property for $\infty$-categories of spans in the generality of Barwick's adequate triples, explicitly describe the cocartesian fibration corresponding to the span functor, and show that the latter restricts to a…
We develop bicategory theory in univalent foundations. Guided by the notion of univalence for (1-)categories studied by Ahrens, Kapulkin, and Shulman, we define and study univalent bicategories. To construct examples of univalent…