We show that the category of graphs has the structure of a 2-category with homotopy as the 2-cells. We then develop an explicit description of homotopies for finite graphs, in terms of what we call ‘spider moves.’ We then create a category by modding out by the 2-cells of our 2-category and use the spider moves to show that for finite graphs, this category is a homotopy category in the sense that it satisfies the universal property for localizing homotopy equivalences. We then show that finite stiff graphs form a skeleton of this homotopy category.

中文翻译：

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图的同伦类别

我们证明图的类别具有2类的结构，同伦作为2个单元。然后，我们用所谓的“蜘蛛移动”来明确描述有限图的同伦。然后，我们通过填充2类的2个单元来创建类别，并使用蜘蛛移动显示对于有限图，该类别在满足局部同伦对等物的通用属性的意义上是同伦类别。然后，我们表明有限的刚性图形成了这一同伦类的骨架。