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In short, the property of being a monomorphism is dual to the property of being an epimorphism. Applying duality, this means that a morphism in some category C is a monomorphism if and only if the reverse morphism in the opposite category C op is an epimorphism. An example comes from reversing the direction of inequalities in a partial order.
Insubordination is the act of willfully disobeying a lawful order of one's superior. It is generally a punishable offense in hierarchical organizations such as the armed forces , which depend on people lower in the chain of command obeying orders.
In category theory, a branch of mathematics, the opposite category or dual category C op of a given category C is formed by reversing the morphisms, i.e. interchanging the source and target of each morphism. Doing the reversal twice yields the original category, so the opposite of an opposite category is the original category itself.
There is a corresponding greatest-lower-bound property; an ordered set possesses the greatest-lower-bound property if and only if it also possesses the least-upper-bound property; the least-upper-bound of the set of lower bounds of a set is the greatest-lower-bound, and the greatest-lower-bound of the set of upper bounds of a set is the least ...
An extrinsic property is not essential or inherent to the subject that is being characterized. For example, mass is an intrinsic property of any physical object , whereas weight is an extrinsic property that depends on the strength of the gravitational field in which the object is placed.
Secretary of State Marco Rubio called out the U.S. Agency for International Development (USAID) on Monday for what he called “rank insubordination,” adding that the agency and its procedures ...
This definition corresponds to the ordinary understanding of a subobject outside category theory. When the category's objects are sets (possibly with additional structure, such as a group structure) and the morphisms are set functions (preserving the additional structure), one thinks of a monomorphism in terms of its image.
In group theory, a branch of mathematics, an opposite group is a way to construct a group from another group that allows one to define right action as a special case of left action. Monoids , groups, rings , and algebras can be viewed as categories with a single object.