Coherence for compact closed categories
WebIt is explained how structures which have arisen in recent work by the present author and Bob Coecke support a notion of scalar which allows quantitative aspects of physical … WebFeb 2, 2024 · The coherence theorem for monoidal categories, like many coherence theorems, has several forms (or, alternatively, refers to several different theorems): …
Coherence for compact closed categories
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WebMay 21, 2000 · In computer science, compact closed categories have appeared as a frame- work for concurrency. The interaction category by Abramsky [1] is such an … Web2.3.1 Prof, the compact closed monoidal weak 2-category of categories, profunctors and ... (1963), and the first coherence theorem (namely, that every monoidal category is equivalent to a strict one) was stated and proved by Lane (1963), and this gives a basis for the relationship between string diagrams and monoidal categories. ...
WebOct 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 ... WebOur purpose is to give an explicit description of the free compact closed category on a given category. A compact closed category is a symmetric monoidal one whose internal …
WebCOMPACT CLOSED BICATEGORIES MICHAEL STAY Abstract. A compact closed bicategory is a symmetric monoidal bicategory where every object is equipped with a weak dual. The unit and counit satisfy the usual “zig-zag” identities of a compact closed category only up to natural isomorphism, and the isomorphism is subject to a … 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 …
WebThe main result of this paper maybe regarded as a coherence theorem for (coherently) compact closed categories. The classical cobordism hypothesis [BD95],[Lur09] informally states that the (framed) 1-Bordism ... A compact closed category is a symmetric monoidal category wherein each object has the spe-cial property of having a left (and hence a ... calories in 12 oz of oat milkWebJun 6, 2012 · The stuff below is mostly due to Chris Schommer-Pries’ definition of symmetric monoidal bicategories together with Day and Street’s definition of a compact closed Gray monoid. Their work, in turn, relies greatly on Paddy McCrudden’s Balanced coalgebroids and a handwritten note for the swallowtail coherence law. In the graphics below, I ... cod and sweetcorn chowderWebApr 7, 2024 · Categories of lenses in computer science, and of open games in compositional game theory, have a structure that is intermediate between symmetric monoidal and compact closed categories. Specifically they have a family of morphisms that behave like the counits of a compact closed category, but have no corresponding … calories in 12 oz of shrimpWebApr 12, 2024 · 摘要： I will talk about the compact intertwining relations for the Volterra operators and Multiplication operators on the Hardy spaces. 34 、王航，华东师范大学. 题目： Delocalized -Betti numbers and higher Kazhdan projections. 摘要： Classical Betti numbers are topological invariants for a closed manifold. Associated to a ... cod and sweet potato recipeWebDec 1, 1980 · I; and Coherence j compact closed categories 209 it is immediate from the explicit description of G v in section 3 that each is of the form (2, f, 0), where 2 is the … calories in 12 oz of orange juiceWebDec 8, 2016 · Unfortunately, the category of locally small cocomplete categories and cocontinuous functors is not closed, as the categories of functors may not be locally … cod and sweet potatoWebJun 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, … cod and two penneth