...and two spaces are of the same homotopy type if and only if they are related by such an equivalence. The ultimate object of algebraic homotopy is to construct...algebraic theory, which is equivalent to homotopy theory in the same sort of way that "analytic" is equivalent to "pure" projective geometry. This book is an...

...indeed that there exists a 'universe' of schematic homotopy types...'. Moreover JHC Whitehead [AH] in his talk at the International Congress of Mathematicians,...algebraic theory, which is equivalent to homotopy theory in the same sort of way that 'analytic' is equivalent to 'pure' projective geometry'. Polyhedra are...