symmetric monoidal categories造句
例句與造句
- A symmetric monoidal category is left closed if and only if it is right closed.
- It is common to extend this case to closed symmetric monoidal categories by using a linear type system.
- Symmetric and orthogonal spectra are arguably the simplest ways to construct a sensible symmetric monoidal category of spectra.
- Other well-known work includes a picture of the octonions as associative in a certain symmetric monoidal category.
- The internal language of closed symmetric monoidal categories is linear logic and the type system is the linear type system.
- It's difficult to find symmetric monoidal categories in a sentence. 用symmetric monoidal categories造句挺難的
- More precisely, one may construct functors between the category of linear type systems and the category of closed symmetric monoidal categories.
- The reason for this is that the CCC is a special case of the closed symmetric monoidal category, which is typically taken to be the category of sets.
- Linear type systems are the internal language of closed symmetric monoidal categories, much in the same way that simply typed lambda calculus is the language of Cartesian closed categories.
- In a symmetric monoidal category, the existence of left duals is equivalent to the existence of right duals, categories of this kind are called ( symmetric ) compact closed categories.
- Mathematically, the basic setup is captured by a dagger symmetric monoidal category : composition of morphisms models sequential composition of processes, and the tensor product describes parallel composition of processes.
- The most famous of these are simply typed lambda calculus, which is the internal language of Cartesian closed categories, and the linear type system, which is the internal language of closed symmetric monoidal categories.
- These isomorphisms make the appropriate category of pointed spaces into a symmetric monoidal category with the smash product as the monoidal product and the pointed 0-sphere ( a two-point discrete space ) as the unit object.
- However, this need not always be the case, as non-symmetric monoidal categories can be encountered in category-theoretic formulations of linguistics; roughly speaking, this is because word-order in natural language matters.
- A "'dagger compact category "'is a dagger symmetric monoidal category \ mathbf { C } which is also compact closed, together with a relation to tie together the dagger structure to the compact structure.
- It is essentially the same universal property shared by all definitions of tensor products, irrespective of the spaces being tensored : this implies that any space with a tensor product is a symmetric monoidal category, and Hilbert spaces are a particular example thereof.
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