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A computer network diagram is a schematic depicting the nodes and connections amongst nodes in a computer network or, more generally, any telecommunications network ...
A monoidal category where every object has a left and right adjoint is called a rigid category. String diagrams for rigid categories can be defined as non-progressive plane graphs, i.e. the edges can bend backward. In the context of categorical quantum mechanics, this is known as the snake equation.
such that the pentagon diagram. and the unitor diagram commute. In the above notation, 1 is the identity morphism of M, I is the unit element and α, λ and ρ are respectively the associativity, the left identity and the right identity of the monoidal category C. Dually, a comonoid in a monoidal category C is a monoid in the dual category C op.
A network's physical topology is a particular concern of the physical layer of the OSI model. Examples of network topologies are found in local area networks , a common computer network installation. Any given node in the LAN has one or more physical links to other devices in the network; graphically mapping these links results in a geometric ...
The category of small categories is a closed monoidal category in exactly two ways: with the usual categorical product and with the funny tensor product. [6] Given two categories and , let be the category with functors,: as objects and unnatural transformations: as arrows, i.e. families of morphisms {: ()} which do not necessarily satisfy the condition for a natural transformation.
This is one of the diagrams used in the definition of a monoidal cateogory. It takes care of the case for when there is an instance of an identity between two objects. commutes. A strict monoidal category is one for which the natural isomorphisms α, λ and ρ are identities. Every monoidal category is monoidally equivalent to a strict monoidal ...
In general, the more interconnections there are, the more robust the network is; but the more expensive it is to install. Therefore, most network diagrams are arranged by their network topology which is the map of logical interconnections of network hosts. Common topologies are: Bus network: all nodes are connected to a common medium along this ...
In category theory, a strong monad is a monad on a monoidal category with an additional natural transformation, called the strength, which governs how the monad interacts with the monoidal product. Strong monads play an important role in theoretical computer science where they are used to model computation with side effects [ 1 ] .
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