We show how to formulate the notion of locally cartesian closed category without chosen pullbacks, by the use of Makkai's theory of anafunctors.
Keywords: anafunctor, axiom of choice, adjoint
2000 MSC: 18A35, 18A40
Theory and Applications of Categories,
Vol. 20, 2008,
No. 1, pp 5-17.
http://www.tac.mta.ca/tac/volumes/20/1/20-01.dvi
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http://www.tac.mta.ca/tac/volumes/20/1/20-01.pdf
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ftp://ftp.tac.mta.ca/pub/tac/html/volumes/20/1/20-01.ps