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Coherence for compact closed categories

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 ... 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 …

Coherence condition - Wikipedia

In 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… 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 … flextronics employees https://vapenotik.com

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Weball satisfying certain coherence conditions. Examples ... The canonical example is the category of sets. Compact closed categories are closed categories. The canonical example is the category FdVect with finite-dimensional vector spaces as objects and linear maps as morphisms. More generally, any monoidal closed category is a closed category. WebCompact closed categories include objects representing higher-order functions and are well-established as models of linear logic, concurrency, and quantum computing. We … 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, … flextronics edi

Note on compact closed categories Journal of the Australian ...

Category:Compact Closed Bicategories The n-Category Café

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Coherence for compact closed categories

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WebIn category theory, a branch of mathematics, dagger compact categories (or dagger compact closed categories) first appeared in 1989 in the work of Sergio Doplicher and John E. Roberts on the reconstruction of compact topological groups from their category of finite-dimensional continuous unitary representations (that is, Tannakian categories). … WebApr 7, 2024 · Categories of polymorphic lenses in computer science, and of open games in compositional game theory, have a curious structure that is reminiscent of compact closed categories, but differs in some crucial ways. Specifically they have a family of morphisms that behave like the counits of a compact closed category, but have no corresponding …

Coherence for compact closed categories

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WebIn mathematics, and particularly category theory, a coherence condition is a collection of conditions requiring that various compositions of elementary morphisms are equal. … 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.

WebNote on compact closed categories - Volume 24 Issue 3. Due to planned system work, ecommerce on Cambridge Core will be unavailable on 12 March 2024 from 08:00 – 18:00 GMT. ... Coherence for compact closed categories. Journal of Pure and Applied Algebra, Vol. 19, Issue. , p. 193. CrossRef; Google Scholar; Shum, Mei Chee 1994. Tortile tensor ... 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. ... 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 …

WebFeb 2, 2024 · The coherence theorem for monoidal categories, like many coherence theorems, has several forms (or, alternatively, refers to several different theorems): …

WebMar 1, 2024 · The category of 1-dimensional cobordisms, freely enriched over the category of commutative monoids and completed with respect to biproducts, provides a proper … chelsea zhang feethttp://www.tac.mta.ca/tac/volumes/37/37/37-37.pdf chelsea zhang baker bottsWebOct 18, 2024 · We prove a strictification theorem for cartesian closed bicategories. First, we adapt Power’s proof of coherence for bicategories with finite bilimits to show that every bicategory with bicategorical cartesian closed structure is biequivalent to a 2-category with 2-categorical cartesian closed structure. chelsea zenit streamingchelsea zhang bodyWebMar 1, 2024 · 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 categories with biproducts and for dagger compact closed categories with dagger biproducts by using the same technique. chelsea zenit predictionWebOur 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 … chelsea zhang motherWebDec 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 … flextronics electronics china