groupoid的音標(biāo)是["gru?p?o?d]，意思是“群范疇”。

基本翻譯：群范疇。

速記技巧：群（group）+ 范疇（范疇名后綴-oid）。

以上信息供您參考，如需了解更多信息，建議查詢(xún)英語(yǔ)詞典或請(qǐng)教專(zhuān)業(yè)英語(yǔ)人士。

Groupoid這個(gè)詞的詞源可以追溯到拉丁語(yǔ)中的“grupus”（群體）和“ideo”（相似）兩個(gè)詞。這個(gè)詞在數(shù)學(xué)中通常被用來(lái)描述一個(gè)對(duì)象集合，其中對(duì)象之間的操作是可逆的，并且滿足群的一些性質(zhì)。

變化形式：在英語(yǔ)中，groupoid通常以復(fù)數(shù)形式出現(xiàn)，即“groupoids”。

相關(guān)單詞：

1. Group (noun)：一個(gè)集合，其中的元素可以執(zhí)行某種特定的操作。

2. Automorphism (noun)：一個(gè)在群或環(huán)中保持元素不變的映射。

3. Homomorphism (noun)：一個(gè)在群或環(huán)中保持元素和操作都相同的映射。

4. Isomorphism (noun)：兩個(gè)對(duì)象或系統(tǒng)之間的相似性，意味著它們?cè)诮Y(jié)構(gòu)或性質(zhì)上非常相似。

5. Symmetry (noun)：物體或系統(tǒng)的一種屬性，意味著它在對(duì)稱(chēng)位置看起來(lái)或感覺(jué)相同。

6. Opposite (adjective)：在方向或順序上與另一事物相反的。

7. Reversal (noun)：一個(gè)過(guò)程的反轉(zhuǎn)或顛倒。

8. Inverse (adjective)：相反的，反過(guò)來(lái)的。

9. Transpose (verb)：將一個(gè)元素或?qū)ο蟮奈恢没蝽樞蜻M(jìn)行交換。

10. Conjugate (verb)：在數(shù)學(xué)中，將元素與其逆元素進(jìn)行交換。

groupoid短語(yǔ)：

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

雙語(yǔ)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.