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###Quantum Computation###

Theory of Systems##

Quantum Computation

Theory of Systems

There have been plenty of applications of category theory in the design of programming languages and programming language theory. Extensive answers can be found on MathOverflow. http://mathoverflow.net/questions/3721/programming-languages-based-on-category-theory) http://mathoverflow.net/questions/4235/relating-category-theory-to-programming-language-theory.

There have been plenty of applications of category theory in the design of programming languages and programming language theory. Extensive answers can be found on MathOverflow. https://mathoverflow.net/questions/3721/programming-languages-based-on-category-theory) https://mathoverflow.net/questions/4235/relating-category-theory-to-programming-language-theory.

Graph transformations can be expressed quite nicely in the language of category theory. This has found application, for example, in model transformation (as in UML models) and other visual modelling formalisms. The approach takes place in the category of graphs and graph homomorphisms. Firstly, a pushout can be seen as a gluing construction: Given two graphs $G_1,G_2$. A graph $P$ and two morphisms $e_1:P\to G_1$ and $e_2:G_2\to P$ denote the parts the two graphs have in common. The pushout unifies these parts, adding in the remaining parts of $G_1$ and $G_2$, in effect, gluing $G_1$ and $G_2$ together along $P$.

Graph transformations can be expressed quite nicely in the language of category theory. This has found application, for example, in model transformation (as in UML models) and other visual modelling formalisms. The approach takes place in the category of graphs and graph homomorphisms. Firstly, a pushout can be seen as a gluing construction: Given two graphs $G_1,G_2$. A graph $P$ and two morphisms $e_1:P\to G_1$ and $e_2:P\to G_2$ denote the parts the two graphs have in common. The pushout unifies these parts, adding in the remaining parts of $G_1$ and $G_2$, in effect, gluing $G_1$ and $G_2$ together along $P$.