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math.AT2006
The fundamental weighted category of a weighted space (From directed to weighted algebraic topology)
Marco Grandis
We want to investigate 'spaces' where paths have a 'weight', or 'cost', expressing length, duration, price, energy, etc. The weight function is not assumed to be invariant up to pa…
math.CT2006★ 11 cited
Categories, norms and weights
Marco Grandis
The well-known Lawvere category R of extended real positive numbers comes with a monoidal closed structure where the tensor product is the sum. But R has another such structure, gi…