Abstract
Let Open image in new window be functors. We know that the class [F, G] of all functorial morphisms from F into G is not always a set, so that we can not speak in general about the category of all functors from Open image in new window into Open image in new window et. But instead of all functors from Open image in new window into Open image in new window we can consider only so-called proper functors, which were defined by Isbell [3]. In this way we can define a category Open image in new window , the category of all proper functors from Open image in new window into Open image in new window . This category contains Open image in new window as a full subcategory and it coincides with the category Open image in new window in the case when Open image in new window is a small category.
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