You are cordially invited to the M.S. Thesis Defense Presentation<\/p>\n
\u201cThomason\u2019s Homotopy Colimit Theorem and Cohomology of Categories\u201d<\/p>\n
Mehmet K\u0131rt\u0131\u015fo\u011flu, M.S. Student in Mathematics<\/p>\n
Abstract: In 1978, R.W. Thomason proves that given a functor F from a small category C to the category of small categories, there is a homotopy equivalence from the homotopy colimit of the nerve of F over C and the nerve of Grothendieck construction over F. We prove that Grothendieck construction is a precofibred category over the canonical functor from the Grothendieck construction to C. We also prove that for any functor \u03c6 : D \u2192 C between arbitrary small categories, there is a homotopy equivalence \u03bb : hocolim_C N(\u03c6\/c) \u2192 N(D) from the homotopy colimit of nerves of left comma categories to nerve of D. We show that these two together proves Thomason\u2019s homotopy colimit theorem from a conceptual point of view.<\/p>\n
We further investigate how our conceptual approximation for the proof of Thomason\u2019s homotopy colimit theorem becomes useful for the cohomology version of Thomason\u2019s theorem which was proven by A. M. Cegarra in 2020.<\/p>\n
Advisor: Prof. Dr. Erg\u00fcn YAL\u00c7IN<\/p>\n
Date: Tuesday, July 2, 2024
\nTime: 14:00
\nPlace: SA 141 \u2013 Mathematics Seminar Room<\/p>\n","protected":false},"excerpt":{"rendered":"
You are cordially invited to the M.S. Thesis Defense Presentation \u201cThomason\u2019s Homotopy Colimit Theorem and Cohomology of Categories\u201d Mehmet K\u0131rt\u0131\u015fo\u011flu, M.S. Student in Mathematics Abstract: In 1978, R.W. Thomason proves that given a functor F from a small category C to the category of small categories, there is a homotopy [\u2026] <\/p>\n