ac.commutative algebra - Filtration over tensor product

clique idea – succesful class of nested rank into rank embeddings retort

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clique idea – succesful class of nested rank into rank embeddings

I pose the next sizable cardinal axiom:

There exists a succesful class of cardinals $lambda$, such that for every $lambda$, there exists a rank into rank embedding $j: V_lambda rightarrow V_lambda$

$textbf{Question}:$ Is the above in keeping with ZFC ? If so, is it equal to any of the rank into rank axioms stronger than I3 ?

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