Prove that the maps that send to the block matrices and are homotopic.
Given a topological space we can construct its suspension . This construction can be lifted to a functor from topological spaces to topological spaces that acts on arrows by sending a continuous map to its suspension which is just in each “level” of the suspensions.
Problem 1: Find two continuous non homotopic maps such that their suspensions are homotopy equivalent.
Problem 2: Find a non nullhomotopic map such that its suspension is nullhomotopic, but now we require the domain and the codomain to be connected!