Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. We introduce some edge (resp. vertex)-homotopy invariants of spatial ...

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 ...

Algebraic structures such as operads, Lie algebras and higher A∞-algebras underpin many foundational aspects of modern mathematics. When combined with homotopy theory—the study of continuous ...