Non-canonical isomorphisms

@article{Lack2009NoncanonicalI,
title={Non-canonical isomorphisms},
author={Stephen Lack},
journal={Journal of Pure and Applied Algebra},
year={2009},
volume={216},
pages={593-597}
}
• S. Lack
• Published 10 December 2009
• Mathematics
• Journal of Pure and Applied Algebra
This result encompasses several results on non-canonical isomorphisms, including Lack's result on normal monoidal functors between braided monoidal categories, since it is applicable in any $2-category of pseudoalgebras, such as the$2$-categories of monoidal Categories, cocomplete categories, pseudofunctors and so on. Categories are coreflectively embedded in multicategories via the "discrete cocone" construction, the right adjoint being given by the monoid construction. Furthermore, the adjunction lifts to the A category C with (countable) biproducts admits summation of countable families of arrows. If this summation is also idempotent, then a version of limit-colimit coincidence holds. In particular, for Given a pseudomonad $$\mathcal {T}$$T, we prove that a lax $$\mathcal {T}$$T-morphism between pseudoalgebras is a $$\mathcal {T}$$T-pseudomorphism if and only if there is a suitable (possibly The collection of open sets of a topological space forms a Heyting algebra, which leads to the idea of a Heyting algebra as a generalized topological space. In fact, a sober topological space may be Categories with countable biproducts are models of the partially additive categories introduced by Manes and Arbib ([3]) as an algebraic semantics for programming languages. They have been also shown Given a pseudomonad T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} Let$\widehat{\mathbb{F}\mathbb{S}et}\$ be the groupoid of finite sets and bijections between them equipped with the canonical symmetric rig category structure given by the disjoint union and the

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