Accessible images revisited

We extend and improve the result of Makkai and Pare that the powerful image of any accessible functor is accessible, assuming there exists a sufficiently large strongly compact cardinal.

[1]  Arthur W. Apter.  Measurability and Degrees of Strong Compactness , 1981, J. Symb. Log..

[2]  Group radicals and strongly compact cardinals , 2013 .

[3]  M. Prest.  Purity, Spectra and Localisation , 2009 .

[4]  Jirí Rosický.  More on directed colimits of models , 1994, Appl. Categorical Struct..

[5]  Joan Bagaria,et al.  On colimits and elementary embeddings , 2013, J. Symb. Log..

[6]  Menachem Magidor,et al.  ON ${\omega _1}$-STRONGLY COMPACT CARDINALS , 2014, J. Symb. Log..

[7]  Will Boney,et al.  TAMENESS FROM LARGE CARDINAL AXIOMS , 2013, The Journal of Symbolic Logic.

[8]  J. Adámek,et al.  Locally presentable and accessible categories , 1994 .

[9]  J. Rosický,et al.  Definable orthogonality classes in accessible categories are small , 2011, 1101.2792.

[10]  G. Raptis,et al.  The accessibility rank of weak equivalences , 2014, 1403.3042.

[11]  D. Cottom.  Purity , 1989, Critical Inquiry.

[12]  Telis K. Menas,et al.  On strong compactness and supercompactness , 1975 .

[13]  J. Rosický,et al.  On Combinatorial Model Categories , 2007, Appl. Categorical Struct..

[14]  Compact cardinals and abelian groups , 1987 .

[15]  Will Boney,et al.  Large Cardinal Axioms from Tameness in AECs , 2015 .

[16]  A. Kanamori.  The Higher Infinite , 1994 .

[17]  Michael Makkai,et al.  Accessible categories: The foundations of categorical model theory, , 2007 .

[18]  Saharon Shelah,et al.  Categoricity of Theories in Lk omega, with k a Compact Ordinal , 1990, Annals of Pure and Applied Logic.

[19]  J. Rosický,et al.  Class-locally presentable and class-accessible categories , 2011, 1110.0605.

[20]  Jirí Rosický,et al.  Classification Theory for Accessible Categories , 2016, J. Symb. Log..

[21]  S. Shelah.  Maximal failures of sequence locality in a.e.c , 2009, 0903.3614.

[22]  Paul C. Eklof.  Almost free modules , 1990 .

[23]  Rami P. Grossberg,et al.  Categoricity from One Successor cardinal in Tame Abstract Elementary Classes , 2006, J. Math. Log..