Independence of the axioms of Quillen's model structure

Key Points

• The aim is to investigate the independence of the axioms in Quillen's model structure.
• Constructed four categories with specific morphism triples.
• Applied the concepts of complete and cocomplete categories.
• Demonstrated how each triple satisfies three axioms but violates the fourth.
• Established that the four axioms in Quillen's model structure are independent.
• Showed that no axiom is a logical consequence of the others.