Related papers: Colax adjunctions and lax-idempotent pseudomonads

We give a summary (without proofs) of the main results in the author's thesis entitled ``Construction of biclosed categories'' (University of New South Wales, Australia, 1970). This summary is reprinted directly from Report 81-0030 of the…

It is shown that the multiplicative monoids of Temperley-Lieb algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a self-adjunction is found in a…

In the first part of this paper we study fibrations of $(\infty,2)$-categories. We give a simple characterization of such fibrations in terms of a certain square being a pullback, and apply this to show that in some cases…

In enriched category theory, the notion of extranatural transformations is more fundamental than that of ordinary natural transformations, and the ends, the universal extranatural transformations, play a critical role. On the other hand,…

We construct explicitly the weights on the simplicial category so that the colimits and limits of 2-functors with those weights provide the Kleisli objects and the Eilenberg-Moore objects, respectively, in any 2-category.

Polynomials in a category have been studied as a generalization of the traditional notion in mathematics. Their construction has recently been extended to higher groupoids, as formalized in homotopy type theory, by Finster, Mimram, Lucas…

Given a group $G$, we define suitable 2-categorical structures on the class of all small categories with $G$-actions and on the class of all small $G$-graded categories, and prove that 2-categorical extensions of the orbit category…

We show how to "interleave" the monad for operads and the monad for contractions on the category \coll of collections, to construct the monad for the operads-with-contraction of Leinster. We first decompose the adjunction for operads and…

We introduce contextads and the Ctx construction, unifying various structures and constructions in category theory dealing with context and contextful arrows -- comonads and their Kleisli construction, actegories and their Para…

Let $\mathbb{A}$ be a $2$-category with suitable opcomma objects and pushouts. We give a direct proof that, provided that the codensity monad of a morphism $p$ exists and is preserved by a suitable morphism, the factorization given by the…

We investigate the properties of lax comma categories over a base category $X$, focusing on topologicity, extensivity, cartesian closedness, and descent. We establish that the forgetful functor from $\mathsf{Cat}//X$ to $\mathsf{Cat}$ is…

We apply the notion of a full convex subcategory to a wide range of algebras including tilted, quasi-tilted, shod, weakly shod, left and right glued, laura, simply connected, strongly simply connected, left supported, and cluster-tilted. In…

We study monoidal 2-categories and bicategories in terms of categorical extensions and the cohomological data they determine in appropriate cohomology theories with coefficients in Picard groupoids. In particular, we analyze the hierarchy…

In this article our main result is a more complete version of the statements obtained in {\rm [6]}. One of the important technical point of our proof is an $\displaystyle L^{2\over m}$ extension theorem of Ohsawa-Takegoshi type, which is…

In this paper we present $2$-category theory from the perspective of Gray-categories using the graphical calculus of separated surface diagrams. As an extended example we consider cones and limits of $2$-functors. Then we use the canonical…

By exploiting the description of topological spaces by either neighborhood systems or filter convergence, we obtain a neighborhood-like presentation of categories of lax algebras. A notable advantage of this approach is that it does not…

We study discrete opfibration classifiers in enhanced 2-categories and show how, under suitable hypotheses, such classifiers can be endowed with the structure of a (lax or pseudo-)T-algebra and classify strict discrete opfibrations in…

We establish the equivalence between models of enhanced $2$-sketches and algebras over monads, including the (co)lax morphisms. More precisely, for any enhanced limit $2$-sketch $\mathbb{T}$ with tight cones, the enhanced $2$-category…

We prove that there is an adjunction between what we call \'etale topological categories and restriction quantal frames that leads to an adjunction with a category of complete restriction monoids. This generalizes the adjunction between…

In this paper, we obtain two extension theorems for cohomology classes and holomorphic sections defined on analytic subvarieties, which are defined as the supports of the quotient sheaves of multiplier ideal sheaves of…