ENGLISH → NEPALI
category
श्रेणी; वर्ग
A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
In a sentence
This steep and dangerous climb belongs to the most difficult category.
यो ठाडो र खतरनाक आरोहण सबैभन्दा कठिन श्रेणीमा पर्छ।
I wouldn’t put this book in the same category as the author’s first novel.
मैं यो पुस्तकलाई लेखकको पहिलो उपन्याससँगै एउटै श्रेणीमा राख्दिनँ।
वस्तुहरूको एउटा सङ्ग्रह, साथै तिनका बीचका क्रमविनिमेय बाणहरूको पारगामी रूपमा संवृत सङ्ग्रह, जसमा प्रत्येक वस्तुको एउटा तत्समक बाण हुन्छ र बाण-संयोजन साहचर्य हुन्छ।
A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.
In a sentence
One well-known category has sets as objects and functions as arrows.
एउटा प्रसिद्ध श्रेणीमा समुच्चयहरू वस्तु र फलनहरू बाण हुन्छन्।
Just as a monoid consists of an underlying set with a binary operation "on top of it" which is closed, associative and with an identity, a category consists of an underlying digraph with an arrow composition operation "on top of it" which is transitively closed, associative, and with an identity at each object. In fact, a category's composition operation, when restricted to a single one of its objects, turns that object's set of arrows (which would all be loops) into a monoid.
जसरी एउटा मोनोइड एउटा अन्तर्निहित समुच्चय र त्यसको माथि एउटा द्विआधारी सञ्चालनबाट बन्छ जो संवृत, साहचर्य र तत्समकयुक्त हुन्छ, त्यसैगरी एउटा श्रेणी एउटा अन्तर्निहित द्विग्राफ र त्यसको माथि एउटा बाण-संयोजन सञ्चालनबाट बन्छ जो पारगामी रूपमा संवृत र साहचर्य हुन्छ तथा प्रत्येक वस्तुमा एउटा तत्समक राख्छ। वास्तवमा, कुनै श्रेणीको संयोजन सञ्चालन, जब त्यसको कुनै एउटा वस्तुमा सीमित गरिन्छ, त्यस वस्तुका बाणहरूको समुच्चय (जो सबै लूप हुनेछन्) लाई एउटा मोनोइडमा बदलिदिन्छ।