In this work, we examine the simplicial morphisms homotopies. Firstly, we give the homotopy of free simplicial morphisms and later show that this homotopy relation indicates an equivalence. Then we ...

In this paper we prove that a map induced from a shape fibration is a shape fibration. We define a fiber shape equivalence relation between shape fibrations. Also, generalizing the homotopy relation, ...

Homotopy theory and K‐theory are intertwined fields that have significantly advanced our understanding of topological spaces, algebraic structures and their interrelations. Homotopy theory studies ...

Knot theory, a branch of topology dedicated to the study of embeddings of circles in three-dimensional space, intersects deeply with homotopy theory—the study of continuous deformations between ...