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In category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object (also called terminal element ): T is terminal if for every object X in C there exists exactly one morphism X → T .
Dually, a final coalgebra is a terminal object in the category of F-coalgebras. The finality provides a general framework for coinduction and corecursion. For example, using the same functor 1 + (−) as before, a coalgebra is defined as a set X together with a function f : X → (1 + X).
Marlin is open source firmware originally designed for RepRap project FDM (fused deposition modeling) 3D printers using the Arduino platform. [1] [2] [3]Once the firmware has been compiled from C++ source code; it is installed and runs on a mainboard with onboard components and general-purpose I/O pins to control and communicate with other components.
A monoid object in [C, C] is a monad on C. For any category with a terminal object and finite products, every object becomes a comonoid object via the diagonal morphism Δ X : X → X × X. Dually in a category with an initial object and finite coproducts every object becomes a monoid object via id X ⊔ id X : X ⊔ X → X.
This is an accepted version of this page This is the latest accepted revision, reviewed on 17 January 2025. General-purpose programming language "C programming language" redirects here. For the book, see The C Programming Language. Not to be confused with C++ or C#. C Logotype used on the cover of the first edition of The C Programming Language Paradigm Multi-paradigm: imperative (procedural ...
In category theory and its applications to mathematics, a biproduct of a finite collection of objects, in a category with zero objects, is both a product and a coproduct. In a preadditive category the notions of product and coproduct coincide for finite collections of objects. [1] The biproduct is a generalization of finite direct sums of modules.
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The Make Controller Kit with an Atmel AT91SAM7X256 microcontroller.. A single-board microcontroller is a microcontroller built onto a single printed circuit board.This board provides all of the circuitry necessary for a useful control task: a microprocessor, I/O circuits, a clock generator, RAM, stored program memory and any necessary support ICs.