Thomason’s Colimit Theorem for the Double Category of Elements

Key Points

• To establish a version of Thomason’s colimit theorem for the double category of elements derived from a 2-functor.
• Defined a 2-category and 2-functor.
• Introduced the double category of elements as proposed by Grandis and Paré.
• Demonstrated weak homotopy equivalence between the hocolim functor and the double category.
• Established the weak homotopy equivalence B(hocolim F) ≃ B(∬_C F).
• Verified that the properties of the double category satisfy those in Thomason’s theorem.