pushout diagram (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun

Phonetic Transcription

/pʊʃˌaʊt ˈdaɪəɡræm/

Meaning and Usage

A "pushout diagram" is a graphical representation used primarily in mathematics and computer science, particularly in category theory and in the context of diagrams in graph theory. It visually illustrates the relationship and morphisms (arrows) between objects and can demonstrate how one structure (object) can be 'pushed out' from another within a particular context. This term is relatively specialized, thus it is less common in everyday usage and is typically found in academic texts and discussions. Its frequency is higher in written contexts, especially in mathematical papers and textbooks rather than in informal oral speech.

Example Sentences

1. The mathematician created a pushout diagram to illustrate the relationship between the two algebraic structures.

2. Математик создал диаграмму "pushout", чтобы проиллюстрировать взаимосвязь между двумя алгебраическими структурами.

3. In the lecture, we examined several examples of pushout diagrams in category theory.

4. На лекции мы рассмотрели несколько примеров диаграмм "pushout" в теории категорий.

5. A pushout diagram helps to visualize the construction of new objects from existing ones in topology.

6. Диаграмма "pushout" помогает визуализировать создание новых объектов из существующих в топологии.

Idiomatic Expressions

The term "pushout diagram" is quite specific and does not typically appear in idiomatic expressions. However, there are terms related to the concept of "push" and "diagram" that may have idiomatic usage:

1. Push the envelope
2. In engineering, it's important to push the envelope when designing new systems to ensure they are innovative.

3. В инженерии важно «толкать границы», когда проектируешь новые системы, чтобы гарантировать их инновационность.

4. Draw a blank

5. When asked for a specific example of a pushout diagram, the student drew a blank and couldn't recall any.

6. Когда его спросили о конкретном примере диаграммы "pushout", студент не смог вспомнить ничего.

7. Hit the nail on the head

8. When the professor explained the pushout diagram clearly, she hit the nail on the head regarding its application.
9. Когда профессор ясно объяснил диаграмму "pushout", она точно указала на ее применение.

Etymology

The term "pushout" combines "push," which derives from Middle English "pushen" meaning to exert force, and "out," indicating the direction of the force. "Diagram," from the Greek "diagramma," meaning a figure or drawing, indicates the graphical representation aspect. The combination suggests a diagram that represents the process of pushing one structure outward from another.

Synonyms and Antonyms

Synonyms: - Commutative diagram - Morphism diagram

Antonyms: - Pullback diagram (though this is a different concept in category theory, it represents a contrasting idea)