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The category Cat has a forgetful functor U into the quiver category Quiv: U : Cat → Quiv. This functor forgets the identity morphisms of a given category, and it forgets morphism compositions. The left adjoint of this functor is a functor F taking Quiv to the corresponding free categories: F : Quiv → Cat
The Common Admission Test (CAT) [1] is a computer based test for admission in graduate management programs. The test consists of three sections: Verbal Ability and Reading Comprehension, Data Interpretation and Logical Reasoning, and Quantitative Ability.
The category Cat consists of all small categories, with functors between them as morphisms. Construction of new categories. Dual category. Any ...
In this context, the standard example is Cat, the 2-category of all (small) categories, and in this example, bimorphisms of morphisms are simply natural transformations of morphisms in the usual sense.
Cat, the category of small categories with functors as morphisms has the empty category, 0 (with no objects and no morphisms), as initial object and the terminal category, 1 (with a single object with a single identity morphism), as terminal object. In the category of schemes, Spec(Z), the prime spectrum of the ring of integers, is a terminal ...
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Arnold's cat map is a particularly well-known example of a hyperbolic toral automorphism, which is an automorphism of a torus given by a square unimodular matrix having no eigenvalues of absolute value 1. [3] The set of the points with a periodic orbit is dense on the torus. Actually a point is periodic if and only if its coordinates are rational.
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