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  1. T

    Can a subcategory be an ideal?

    Consider a category C with objects ob(C) and morphisms hom(C). Suppose there is a subcategory D such that ob(D)=ob(C) but hom(D) is a subset of hom(C), with the property that the product of two morphisms in hom(C), f*g, is an element of hom(D) if either f or g is in hom(D). This subcategory is...
  2. T

    Projection onto the kernel of a matrix

    If we have a matrix M with a kernel, in many cases there exists a projection operator P onto the kernel of M satisfying [P,M]=0. It seems to me that this projector does not in general need to be an orthogonal projector, but it is probably unique if it exists. My question: is there a standard...