Recent advancements in graph theory often incorporate the concept of graph products. The concept of the categorical product of graphs was introduced by the mathematician Frank Harary in his paper titled "Topological Concepts for Maximum Graphs" published in 1969. The categorical product of graphs can be used to model and analyze complex network topologies. By considering the product of individual components, such as nodes or edges, one can study the interconnections and properties of the overall network structure. In light of this, our study aims to explore the properties of the categorical product of two graphs and demonstrate that the categorical products of two-cycle graphs with odd lengths are 2-connected.