My thoughts and analysis on 2013 are probably going to be controversial on here. I have a feeling that the notion that 2013 was completely removed from the 2000's is exaggerated on here and inthe00s.
Culturally: In a way, I agree with the notion:*Dubstep, electropop, and the first age of neo-teen pop finally fade out by Spring 2013.
*Vine, Instagram, and Snapchat grow in popularity throughout 2013.
*Rage Comics and Nyan Cat were basically gone by 2013.
*The hipster trend rises to greater proportions in 2013, but I thought that it peaked in 2015 when hipsters were basically everywhere.
*The age of "twerking" ushers in with Miley Cyrus at the 2013 VMA.
*The whole cultural atmosphere seemed to lack the "brightness" that 2008-2012 had.
However, there are still some things culturally that make the notion disagreeable, especially with early 2013:*There was still some cheesiness to the year with songs like "What Does The Fox Say?" by Ylvis, "Best Song Ever" by One Direction, and all of Alison Gold's releases.
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Breaking Bad and
Dexter were still on air in early 2013.
*Musical.ly, one of the largest Gen Z apps (Loren Gray, Baby Ariel, Jamie Rose, Cole LaBrant, the Mantler twins, and Jayden Croes are all famous Zeds that use Musical.ly) did not exist yet in 2013.
Politically, it is somewhat disagreeable:*It was the last year before SJWs and the Alt-right.
*ISIS was not heard of yet.
*Even though Black Lives Matter started in 2013, it would become much more prevalent in 2014, especially after the shooting of Michael Brown.
*The Ebola crisis was unheard of in the US until March 2014.
*Crimea was still unheard of in 2013.
*Even though Colorado and Washington legalized recreational marijuana use in 2012, there were still no legal recreational sales of marijuana until 2014.
*Altogether, 2013 still felt "normal", especially in comparison with the years that came after.
Conclusion:2013 is definitely "core 2010's", but to say that it was completely 2010's is a bit of a stretch in my opinion.
*If there was a 90's equivalent of 2013, it'd probably be 1992.
*If there was a 2000's equivalent of 2013, it'd probably be 2003.