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
New Structures for Physics - Google Books
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