Basic Elements of Abstract Homotopy Theory

Mehmet Akif Erdal, Bilkent University.
Date: 21st of March, 2018, Wednesday. Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: Abstract homotopy theory, also known as homotopical algebra, provides a framework that allows us to use tools from homotopy theory in various different settings, ranging from representation theory to mathematical physics. For short, it is the study of everything that is related with higher categories. This talk will be a motivational introduction to the subject. We will discuss some of the main purposes of abstract homotopy theory and state some basic definitions and examples. In particular, we will talk about definitions of categories with weak equivalences, homotopical categories and their homotopy category and we will discuss existence of the homotopy category. Later, if the time permits, we state some of the difficulties in the construction of homotopy categories and discuss why we need extra structures, such as model categories or (co)fibration categories.