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Resumen: Lawvere's Elementary Theory of the Category of Sets (ETCS) was conceived as an alternative to ZFC that represents more accurately how mathematicians actually do mathematics. But can ETCS do everything that ZFC can? I will present some evidence that yes, it can. Specifically, I will sketch how the beginning of the theory of large cardinals looks in ETCS, describing both the similarities and the differences between the two approaches. No prior familiarity with ETCS will be assumed.
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