pointlike groupoid (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun

Phonetic Transcription

/pɔɪntlaɪk ˈɡruːpɔɪd/

Meaning and Usage

A pointlike groupoid refers to a type of mathematical structure used in category theory and algebra. Specifically, a groupoid is a category in which every morphism (or arrow) is invertible. A "pointlike groupoid" suggests that the groupoid behaves similarly to a discrete collection of points rather than having more complex structures. This term is used primarily in academic and theoretical contexts, particularly in mathematics and theoretical physics. Its frequency of use is relatively low, mainly confined to specialized literature rather than everyday conversation.

Example Sentences: 1. The mathematician defined a pointlike groupoid to illustrate the concept of invertible morphisms. - La matemàtica va definir un grupoid semblant a un punt per il·lustrar el concepte de morfismes invertibles.

1. In the study of topological spaces, a pointlike groupoid can simplify the analysis of continuous transformations.

2. En l'estudi dels espais topològics, un grupoid semblant a un punt pot simplificar l'anàlisi de les transformacions continuïtat.

3. Researchers explored the properties of a pointlike groupoid in relation to higher-dimensional algebraic structures.

4. Els investigadors van explorar les propietats d'un grupoid semblant a un punt en relació amb estructures algebraiques de dimensions superiors.

Idiomatic Expressions

While "pointlike groupoid" is a specialized mathematical term and not commonly used in idiomatic expressions, it can be associated with phrases related to abstraction and theoretical considerations in mathematics. Here are some sentences that convey related idiomatic meanings:

1. In higher algebra, the theory often begins with pointlike groupoids as a foundation.

2. En álgebra superior, la teoria sovint comença amb grupoids semblants a un punt com a fonament.

3. The concept of pointlike groupoids opens new horizons in category theory.

4. El concepte de grupoids semblants a un punt obre nous horitzons en la teoria de categories.

5. When discussing symmetries in physics, we often encounter pointlike groupoids and their implications.

6. Quan discutim simetries en física, sovint ens trobem amb grupoids semblants a un punt i les seves implicacions.

Etymology

The term "groupoid" comes from the combination of "group" (from the Latin "gens," meaning "people," formalized in mathematics to denote a set with an operation satisfying certain axioms) and the suffix "-oid" (from the Greek "eidos," meaning "form" or "shape"). The prefix "pointlike" indicates resemblance to a point, emphasizing the simplicity and individuality of the structure referred to.

Synonyms and Antonyms

Synonyms: - Discrete groupoid - Simple category - Invertible category structure

Antonyms: - Non-invertible category - Complex groupoid - Continuous structure

Overall, "pointlike groupoid" is a technical term primarily used in mathematical discussions, often requiring specific contextual background to fully grasp its implications and applications.