This is a (not so brief) intro to simplicial sets, designed to hopefully give some background for this week's ACT reading.
In case you already know some of this stuff and want to skip ahead, here's the outline:
00:00-20:03 definition(s) of simplicial sets + how we think about them
20:03-38:09 example 1: the standard simplicial sets + why they motivate the way we picture all simplicial sets
38:09-43:58 example 2: the nerve of a category
43:58- 54:18 segal maps
54:18- 55:52 a word about simplicial objects