Mapping Cylinders and Mapping Cones

This lecture delves into the construction of mapping cylinders and cones, exploring their role in the theory of exact sequences. The instructor discusses the process of mapping cylinders as quotients of a cylinder on X, and mapping cones as suspensions of a map. By iterating these constructions, a sequence of spaces is formed, showcasing H-cof exactness. The lecture also covers the push-out construction and the identification of the suspension of a map. Through detailed diagrams and explanations, the audience gains insights into how these concepts are applied in topology.