Span (Category Theory)
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High Quality Content by WIKIPEDIA articles! A span, in category theory, is a generalization of the notion of relation between two objects of a category. When the category has all pullbacks (and satisfies a small number of other conditions), spans can be considered as morphisms in a category of fractions. Thus it consists of three objects X, Y and Z of C and morphisms f:Y X and g:Z X: it is two maps with common codomain. The limit of a cospan is a pullback.An example of a cospan is a cobordism W between two manifolds M and N, where the two maps are the inclusions into W. Note that while cobordi...
High Quality Content by WIKIPEDIA articles! A span, in category theory, is a generalization of the notion of relation between two objects of a category. When the category has all pullbacks (and satisfies a small number of other conditions), spans can be considered as morphisms in a category of fractions. Thus it consists of three objects X, Y and Z of C and morphisms f:Y X and g:Z X: it is two maps with common codomain. The limit of a cospan is a pullback.An example of a cospan is a cobordism W between two manifolds M and N, where the two maps are the inclusions into W. Note that while cobordisms are cospans, the category of cobordisms is not a "cospan category": it is not the category of all cospans in "the category of manifolds with inclusions on the boundary", but rather a subcategory thereof, as the requirement that M and N form a partition of the boundary of W is a global constraint.
