Topology IV.b - homotopy theory

Homework/Semi-flipped teaching. Since we couldn't reach the part about homotopy pushouts, same homework as for Week 9: I would like you to read the beginning of the section 6 about pushouts, alternatively watch the second half of the video from Week 9:

https://mediaspace.epfl.ch/media/Whitehead+Theorem%2C+Lecture09.2/0_gzcv14yl

It starts after 26 minutes and ends at minute 44. I will finish explaining what I wanted to say about left properness and use it then to show that homotopy pushouts are homotopy invariant. We will continue with examples and computations of homotopy pushouts before dualizing the part about cofibrations and introduce fibrations.