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The relationship between opposites is known as opposition. A member of a pair of opposites can generally be determined by the question What is the opposite of X ? The term antonym (and the related antonymy) is commonly taken to be synonymous with opposite, but antonym also has other more restricted meanings. Graded (or gradable) antonyms are ...
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.
In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite category C op.Given a statement regarding the category C, by interchanging the source and target of each morphism as well as interchanging the order of composing two morphisms, a corresponding dual statement is obtained regarding the opposite ...
Therefore, it is not opposite day, but if you say it is a normal day it would be considered a normal day, which contradicts the fact that it has previously been stated that it is an opposite day. Richard's paradox : We appear to be able to use simple English to define a decimal expansion in a way that is self-contradictory.
A functor F : C → D yields an equivalence of categories if and only if it is simultaneously: . full, i.e. for any two objects c 1 and c 2 of C, the map Hom C (c 1,c 2) → Hom D (Fc 1,Fc 2) induced by F is surjective;
In linguistics, converses or relational antonyms are pairs of words that refer to a relationship from opposite points of view, such as parent/child or borrow/lend. [ 1 ] [ 2 ] The relationship between such words is called a converse relation . [ 2 ]
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.
In mathematics, the converse of a theorem of the form P → Q will be Q → P. The converse may or may not be true, and even if true, the proof may be difficult. For example, the four-vertex theorem was proved in 1912, but its converse was proved only in 1997. [3]