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• W569857046 abstract "We extend and improve the result of Makkai and Paré (1989) that the powerful image of any accessible functor <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=application/x-tex>F</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is accessible, assuming there exists a sufficiently large strongly compact cardinal. We reduce the required large cardinal assumption to the existence of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Subscript mu comma omega> <mml:semantics> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>μ<!-- μ --></mml:mi> <mml:mo>,</mml:mo> <mml:mi>ω<!-- ω --></mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding=application/x-tex>L_{mu ,omega }</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-compact cardinals for sufficiently large <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=mu> <mml:semantics> <mml:mi>μ<!-- μ --></mml:mi> <mml:annotation encoding=application/x-tex>mu</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and also show that under this assumption the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=lamda> <mml:semantics> <mml:mi>λ<!-- λ --></mml:mi> <mml:annotation encoding=application/x-tex>lambda</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-pure powerful image of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=application/x-tex>F</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is accessible. From the first of these statements, we obtain that the tameness of every Abstract Elementary Class follows from a weaker large cardinal assumption than was previously known. We provide two ways of employing the large cardinal assumption to prove each result — one by a direct ultraproduct construction and one using the machinery of elementary embeddings of the set-theoretic universe." @default.
• W569857046 created "2016-06-24" @default.
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• W569857046 date "2016-11-18" @default.
• W569857046 modified "2023-10-17" @default.
• W569857046 title "Accessible images revisited" @default.
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• W569857046 doi "https://doi.org/10.1090/proc/13190" @default.
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