标题： 图示集中的等价关系 显示英文标题

标题： Equivalences in diagrammatic sets

摘要： 我们证明了图示集，一种拓扑上合理的多边形和严格$\omega$-范畴的替代方法，在共归纳弱可逆性的意义上，具有内部等价的概念。 我们证明了等价具有预期的性质：它们包含所有退化的单元，对于 2-out-of-3 是封闭的，并且满足适当的“除法引理”版本，这确保了在所有边上用等价包裹一个图示是一个在更高等价下的可逆操作。 在得到这一结果的过程中，我们开发了方法，例如自然等价的代数演算，用于处理弱单位和单位者，这些是该框架与严格$\omega$-范畴不同的地方。 显示英文摘要

摘要： We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the expected properties: they include all degenerate cells, are closed under 2-out-of-3, and satisfy an appropriate version of the "division lemma", which ensures that enwrapping a diagram with equivalences at all sides is an invertible operation up to higher equivalence. On the way to this result, we develop methods, such as an algebraic calculus of natural equivalences, for handling the weak units and unitors which set this framework apart from strict $\omega$-categories.