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At Directed Algebraic Topology, Victor has asked
Is it necessary to know regular (nondirected) algebraic topology before reading this book? How much advanced category theory it requires?
This seems easier to reply to here so I have left a pointed there.
Marco Grandis’s book does not need a great knowledge of classical algebraic topology. It does assume some knowledge of his approaches to Abstract Homotopy Theory. There will be a book published shortly which will look at some of the same questions from a more ‘computer science’ viewpoint. (This will be by Eric Goubault and a group of his collaborators.) To understand the subject of directed homotopy theory I would look at some survey articles and theses from the group working at the École Polytechnique, but to get to understand the abstract homotopy theory of directed spaces, then perhaps looking at Grandis’s papers first would be a good idea as the book is constructed from several of his papers plus new linking material.
You say, I need Abstract Homotopy Theory but don’t meed classical algebraic topology, as a prerequisite.
What is the difference between Abstract Homotopy Theory and classical algebraic topology?
Good question. Classical algebraic topology looks at invariants of spaces via certain functors to well known categories of usually algebraic objects (groups, algebras, etc.). Abstract homotopy theory studies the characteristics of that modelling process. You do not NEED abstract homotopy theory but Grandis does assume a passing knowledge of the types of properties that are given in some of his earlier books.
My advice would be to get hold of his papers on directed homotopy and glance at them to see if they do what you need.
I have transferred a query from Directed Algebraic Topology and removed it from the n-Lab page.
Eric: Does anyone here know Professor Grandis well enough to invite him here? I’m a fan and would love to see him participate in the n-Community.
Tim: I am an old friend of Marco, but do not think that any direct involvement is likely.
I will be writing a review of the book for the Canadian math. Soc. so may be able to contribute something to this later on.
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