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The concept of monoidal category does not presume that values of such aggregate types can be taken apart; on the contrary, it provides a framework that unifies classical and quantum information theory. [1] In category theory, monoidal categories can be used to define the concept of a monoid object and an associated action on the objects of the ...
In category theory, a branch of mathematics, a monoid (or monoid object, or internal monoid, or algebra) (M, μ, η) in a monoidal category (C, ⊗, I) is an object M together with two morphisms. μ: M ⊗ M → M called multiplication, η: I → M called unit, such that the pentagon diagram. and the unitor diagram commute.
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Download as PDF; Printable version; ... Category theory is a mathematical theory that deals in an abstract way with mathematical ... Monoidal categories (40 P) O. ...
This is a glossary of properties and concepts in category theory in mathematics. (see also Outline of category theory.). Notes on foundations: In many expositions (e.g., Vistoli), the set-theoretic issues are ignored; this means, for instance, that one does not distinguish between small and large categories and that one can arbitrarily form a localization of a category. [1]
Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. [1] Category theory is used in almost all areas of mathematics.
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Download as PDF; Printable version; ... Pages in category "Monoidal categories" ... Center (category theory) Closed monoidal category;