60 citations · 92 across the 10 of their papers we have counts for
10 papers
Intercategories
Marco Grandis, Robert Paré
We introduce a 3-dimensional categorical structure which we call intercategory. This is a kind of weak triple category with three kinds of arrows, three kinds of 2-dimensional cell…
Homotopy spectral sequences
Marco Grandis
In homotopy theory, exact sequences and spectral sequences consist of groups and pointed sets, linked by actions. We prove that the theory of such exact and spectral sequences can…
Cubical cospans and higher cobordisms (Cospans in algebraic topology, III)
Marco Grandis
After two papers on weak cubical categories and {\it collarable} cospans, respectively, we put things together and construct a {\it weak} cubical category of cubical {\it collared}…
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…
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…
Directed homotopy theory, I. The fundamental category
Marco Grandis
Directed Algebraic Topology is beginning to emerge from various applications. The basic structure we shall use for such a theory, a 'd-space', is a topological space equipped with…