Quotients of span categories that are allegories and the representation of regular categories

  title={Quotients of span categories that are allegories and the representation of regular categories},
  author={S. N. Hosseini and Amir R. Shir Ali Nasab and Walter Tholen and Leila Yeganeh},
We consider the ordinary category Span(C) of (isomorphism classes of) spans of morphisms in a category C with finite limits as needed, composed horizontally via pullback, and give a general criterion for a quotient of Span(C) to be an allegory. In particular, when C carries a pullback-stable, but not necessarily proper, (E ,M)factorization system, we establish a quotient category SpanE(C) that is isomorphic to the category RelM(C) ofM-relations in C, and show that it is a (unitary and tabular… 
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