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- [T]he issue of comparing definitions of weak n-category is a slippery one, as it is hard to say what it even means for two such definitions to be equivalent. [...] It is widely held that the structure formed by weak n-categories and the functors, transformations, ... between them should be a weak -category; and if this is the case then the question is whether your weak -category of weak n-categories is equivalent to mine—but whose definition of weak -category are we using here... ? (en)
- The theory of categories originated ... with the need to guide complicated calculations involving passage to the limit in the study of the qualitative leap from spaces to homotopical/homological objects. ... But category theory does not rest content with mere classification in the spirit of Wolffian metaphysics ; rather it is the mutability of mathematically precise structures which is the essential content of category theory. (en)
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