Type theory and homotopy theory have evolved into profoundly interconnected disciplines. Type theory, with its foundations in logic and computer science, provides a formal language for constructing ...

Cobordism theory, a cornerstone of geometric topology, analyses the equivalence classes of manifolds by utilising the concept of cobordism – whereby two manifolds are considered equivalent if they ...

Abstract: We present two seemingly different definitions of constructive ordinal exponentiation, where an ordinal is taken to be a transitive, extensional, and wellfounded order on a set. The first ...