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Whenever I've seen the definition was of the classifying space of a category, the category is always specified to be small. I understand the definition well enough for my purposes (I think), but it occurred to me today, why small? Is there a reason we only take nerves of small categories? Does the definition fail of if the objects are too big? |
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Classifying space of large category?Whenever I've seen the definition was the classifying space of a category, the category is always specified to be small. I understand the definition well enough for my purposes (I think), but it occurred to me today, why small? Is there a reason we only take nerves of small categories? Does the definition fail of the objects are too big?
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