Tensors, multivectors, wedge products, multilinear maps, exterior (Grassmann) algebras.

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Co-ends as a trace operation on profunctors

The n-lab site on profunctors (http://ncatlab.org/nlab/show/profunctor) describes profunctor composition as using a co-end to "trace out" the connecting variable: $F\circ G := \int^{d\in D} F(-, d) ...