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The physical network topology can be directly represented in a network diagram, as it is simply the physical graph represented by the diagrams, with network nodes as vertices and connections as undirected or direct edges (depending on the type of connection). [3]
Physical topology is the placement of the various components of a network (e.g., device location and cable installation), while logical topology illustrates how data flows within a network. Distances between nodes, physical interconnections, transmission rates , or signal types may differ between two different networks, yet their logical ...
In topology, a branch of mathematics, a topological monoid is a monoid object in the category of topological spaces. In other words, it is a monoid with a topology with respect to which the monoid's binary operation is continuous. Every topological group is a topological monoid.
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.
The monoidal product of two diagrams is represented by placing one diagram above the other. Indeed, all ZX-diagrams are built freely from a set of generators via composition and monoidal product, modulo the equalities induced by the compact structure and the rules of the ZX-calculus given below.
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 ...
Star topology in use in a network. A star network is an implementation of a spoke–hub distribution paradigm in computer networks. In a star network, every host is connected to a central hub. In its simplest form, one central hub acts as a conduit to transmit messages. [1] The star network is one of the most common computer network topologies.
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 ] .