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Dec 24, 2021 at 6:43 comment added kdog I added some notes to my question based on this answer. I think this explains also why I confused $j_1(j_2\mid R_\gamma)$ with the pointwise image.
Dec 23, 2021 at 19:47 comment added kdog Thank you for the clearing up a number of misconceptions and thanks @monroe-eskew. Note that because $j_1(\gamma)\ge\gamma)$, $R_{j_1(\gamma)}$ contains $R_\gamma$ which insures $j_1$ is total on $R_\lambda$. These elementary embeddings of set theory or huge parts of it really take some getting used to.
Dec 23, 2021 at 19:43 vote accept kdog
Dec 22, 2021 at 13:12 history answered Peter LeFanu Lumsdaine CC BY-SA 4.0