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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.
A biological network is a method of representing systems as complex sets of binary interactions or relations between various biological entities. [1] In general, networks or graphs are used to capture relationships between entities or objects. [1]
Topology Analysis analyzes the topology of a network to identify relevant participates and substructures that may be of biological significance. The term encompasses an entire class of techniques such as network motif search, centrality analysis, topological clustering, and shortest paths. These are but a few examples, each of these techniques ...
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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 category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general monoidal category.It is motivated by the observation that, in many practical applications, the hom-set often has additional structure that should be respected, e.g., that of being a vector space of morphisms, or a topological space of morphisms.
However final topology is not the only criterion for defining transmembrane protein groups, rather location of topogenic determinants and mechanism of assembly is considered in the classification [2] Several databases provide experimentally determined topologies of membrane proteins. They include Uniprot, TOPDB, [3] [4] [5] OPM, and ExTopoDB.