What does categorical dual mean?
Definitions for categorical dual
cat·e·gor·i·cal du·al
This dictionary definitions page includes all the possible meanings, example usage and translations of the word categorical dual.
Wiktionary
categorical dualnoun
For a given category C, its dual category C is obtained by reversing the direction of each one of the arrows of C.
Wikipedia
categorical dual
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 Cop. 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 category Cop. Duality, as such, is the assertion that truth is invariant under this operation on statements. In other words, if a statement is true about C, then its dual statement is true about Cop. Also, if a statement is false about C, then its dual has to be false about Cop. Given a concrete category C, it is often the case that the opposite category Cop per se is abstract. Cop need not be a category that arises from mathematical practice. In this case, another category D is also termed to be in duality with C if D and Cop are equivalent as categories. In the case when C and its opposite Cop are equivalent, such a category is self-dual.
Numerology
Chaldean Numerology
The numerical value of categorical dual in Chaldean Numerology is: 2
Pythagorean Numerology
The numerical value of categorical dual in Pythagorean Numerology is: 6
Translations for categorical dual
From our Multilingual Translation Dictionary
- κατηγορηματικό διπλόGreek
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"categorical dual." Definitions.net. STANDS4 LLC, 2024. Web. 14 May 2024. <https://www.definitions.net/definition/categorical+dual>.
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