groupoid

groupoid的音标是["gruːpɪoɪd]，意思是“群范畴”。

基本翻译：群范畴。

速记技巧：群（group）+ 范畴（范畴名后缀-oid）。

以上信息供您参考，如需了解更多信息，建议查询英语词典或请教专业英语人士。

Groupoid这个词的词源可以追溯到拉丁语中的“grupus”（群体）和“ideo”（相似）两个词。这个词在数学中通常被用来描述一个对象集合，其中对象之间的操作是可逆的，并且满足群的一些性质。

变化形式：在英语中，groupoid通常以复数形式出现，即“groupoids”。

相关单词：

1. Group (noun)：一个集合，其中的元素可以执行某种特定的操作。

2. Automorphism (noun)：一个在群或环中保持元素不变的映射。

3. Homomorphism (noun)：一个在群或环中保持元素和操作都相同的映射。

4. Isomorphism (noun)：两个对象或系统之间的相似性，意味着它们在结构或性质上非常相似。

5. Symmetry (noun)：物体或系统的一种属性，意味着它在对称位置看起来或感觉相同。

6. Opposite (adjective)：在方向或顺序上与另一事物相反的。

7. Reversal (noun)：一个过程的反转或颠倒。

8. Inverse (adjective)：相反的，反过来的。

9. Transpose (verb)：将一个元素或对象的位置或顺序进行交换。

10. Conjugate (verb)：在数学中，将元素与其逆元素进行交换。

groupoid短语：

1. groupoid of transformations

2. groupoid of permutations

3. groupoid of equivalence classes

4. groupoid of congruence classes

5. groupoid of isomorphisms

6. groupoid of homomorphisms

7. groupoid of automorphisms

双语例句：

1. The groupoid of transformations is a mathematical concept that deals with the study of transformations between objects.

2. The groupoid of permutations is a mathematical tool that helps us to understand the order of events or objects.

3. The groupoid of equivalence classes is used to classify objects based on their similarity or difference.

4. The groupoid of congruence classes is a mathematical tool that helps us to understand the relationship between objects and their transformations.

5. Groupoids are used in category theory to study the relationships between objects and their morphisms.

6. Groupoids are also used in physics to describe symmetry transformations in quantum mechanics and other areas.

7. Groupoids are a powerful tool for studying the relationships between objects and their properties in mathematics and other disciplines.

英文小作文：Groupoids in Modern Mathematics

Groupoids are a fascinating topic in modern mathematics, playing a crucial role in many branches of the discipline. They provide a powerful tool for studying the relationships between objects and their properties, and are particularly useful in describing symmetry transformations and other mathematical concepts.

In category theory, groupoids serve as a foundation for understanding the relationships between different types of objects and their morphisms. They provide a framework for classifying and understanding mathematical structures, allowing for a more systematic approach to studying various mathematical concepts.

Moreover, groupoids are also used in physics to describe symmetry transformations in quantum mechanics and other areas of research. By using groupoids, physicists can better understand the relationships between different systems and their interactions, leading to more accurate and reliable models of physical phenomena.

Overall, groupoids serve as an indispensable tool for studying the relationships between objects and their properties in mathematics and other disciplines, providing a valuable resource for advancing our understanding of the world around us.