What does semigroupoid mean?
Definitions for semigroupoid
semi·groupoid
This dictionary definitions page includes all the possible meanings, example usage and translations of the word semigroupoid.
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Wiktionary
semigroupoidnoun
A form of partial algebra in category theory
Wikidata
Semigroupoid
In mathematics, a semigroupoid is a partial algebra which satisfies the axioms for a small category, except possibly for the requirement that there be an identity at each object. Semigroupoids generalise semigroups in the same way that small categories generalise monoids and groupoids generalise groups, and have applications in the structural theory of semigroups. Formally, a semigroupoid consists of: ⁕a set of things called objects. ⁕for every two objects A and B a set Mor of things called morphisms from A to B. If f is in Mor, we write f : A → B. ⁕for every three objects A, B and C a binary operation Mor × Mor → Mor called composition of morphisms. The composition of f : A → B and g : B → C is written as g o f or gf. such that the following axiom holds: ⁕ if f : A → B, g : B → C and h : C → D then h o = o f. Although the axioms defining a single semigroup are almost identical to those defining a category, one frequently assumes many additional facts about the relationship between categories. The term "semigroup" does not imply any of these assumptions.
Numerology
Chaldean Numerology
The numerical value of semigroupoid in Chaldean Numerology is: 6
Pythagorean Numerology
The numerical value of semigroupoid in Pythagorean Numerology is: 7
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"semigroupoid." Definitions.net. STANDS4 LLC, 2024. Web. 19 Mar. 2024. <https://www.definitions.net/definition/semigroupoid>.
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