Coherence for compact closed categories
WebJan 15, 2011 · This volume provides a series of tutorials on mathematical structures which recently have gained prominence in physics, ranging from quantum foundations, via quantum information, to quantum gravity. These include the theory of monoidal categories and corresponding graphical calculi, Girard’s linear logic, Scott domains, lambda calculus …
Coherence for compact closed categories
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WebSep 24, 2008 · Abramsky and Coecke (Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, pp. 415–425, IEEE Comput. Soc., New York, 2004) have recently introduced an approach to finite dimensional quantum mechanics based on strongly compact closed categories with biproducts. In this note it is shown that the projections … WebJan 27, 2024 · Abstract: A coherence result for symmetric monoidal closed categories with biproducts is shown in this paper. It is explained how to prove, by using the …
Web2. A 2-categorical approach to coherence in compact closed categories A compact closed category is a symmetric monoidal category wherein each object has the special property of having a left (and hence a right) dual. We begin by recalling the de nition of a … WebJun 29, 2024 · There has been a fair body of research devoted to displaying several variants of monoidal categories using a graphical language. For instance, diagrammatic reasoning for compact closed categories was introduced and shown to be coherent by Kelly and Laplaza [], and the research of Joyal and Street has led to graphical languages for, …
WebCoherence for compact closed categories - CORE Reader WebOct 16, 2024 · The construction of a model category of coherently compact closed categories leads to a proof of the one dimensional cobordism hypothesis based on a …
WebAbstract. A coherence result for symmetric monoidal closed categories with biproducts is shown in this paper. It is also explained how to prove coherence for compact closed …
WebJan 27, 2024 · Dagger compact closed categories were recently introduced by Abramsky and Coecke, under the name “strongly compact closed categories”, as an axiomatic framework for quantum mechanics. class diagram for libraryIn category theory, a branch of mathematics, compact closed categories are a general context for treating dual objects. The idea of a dual object generalizes the more familiar concept of the dual of a finite-dimensional vector space. So, the motivating example of a compact closed category is FdVect, the category having finite-dimensional vector spaces as objects and linear maps as morphisms, with tensor product as the monoidal structure. Another example is Rel, the category h… download latest minecraft launcherWebJan 27, 2024 · A coherence result for symmetric monoidal closed categories with biproducts is shown in this paper. It is explained how to prove, by using the same … class diagram for library managementWebThe category $$\mathcal{D}\mathcal{Y}\left( \mathcal{C} \right)_A^A $$ of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. ... Coherence for compact closed categories, J. Pure Appl. Algebra 19 (1980), 193–213. Article Google Scholar Lambe, L. A. and Radford ... class diagram for exam management systemWebOct 16, 2024 · W e recall that a compact closed category C is a closed symmetric monoidal category wherein the internal hom object, between two objects c 1 , c 2 ∈ C is defined as follows: [ c 1 , c 2 ] C ... download latest miracle box setupWebDec 8, 2016 · In the article "Coherence for compact closed categories", Kelly and Laplaza say The “category” of small categories and profunctors fails to be a compact closed category only because it fails to be an honest … class diagram for instagramWebCompact closed categories include objects representing higher-order functions and are well-established as models of linear logic, concurrency, and quantum computing. We … class diagram for hotel booking system