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2. Equivalence of categories - Wikipedia

   en.wikipedia.org/wiki/Equivalence_of_categories

   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;

3. Equivalence relation - Wikipedia

   en.wikipedia.org/wiki/Equivalence_relation

   Then the following three connected theorems hold: [10] ~ partitions A into equivalence classes. (This is the Fundamental Theorem of Equivalence Relations, mentioned above); Given a partition of A, G is a transformation group under composition, whose orbits are the cells of the partition; [14]

4. Equality (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Equality_(mathematics)

   Then the relation x R y is equivalent with the equality x R = y R. It follows that equality is the finest equivalence relation on any set S in the sense that it is the relation that has the smallest equivalence classes (every class is reduced to a single element). In some contexts, equality is sharply distinguished from equivalence or ...

5. Turpin case - Wikipedia

   en.wikipedia.org/wiki/Turpin_case

   The Turpin case involved the abuse of children and dependent adults by their parents, David and Louise Turpin of Perris, California, U.S. The ages of the 13 victims ranged from 2 to 29 years-old. On January 14, 2018, one of the daughters, then-17-year-old Jordan Turpin , escaped and called local police, who then raided the residence and ...

6. Congruence relation - Wikipedia

   en.wikipedia.org/wiki/Congruence_relation

   In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements. [1]

7. Legality of child pornography - Wikipedia

   en.wikipedia.org/wiki/Legality_of_child_pornography

   Child pornography is illegal in most countries, but there is substantial variation in definitions, categories, penalties, and interpretations of laws. Differences include the definition of "child" under the laws, which can vary with the age of sexual consent; the definition of "child pornography" itself, for example on the basis of medium or degree of reality; and which actions are criminal (e ...