A categorical version of the Brouwer–Heyting–Kolmogorov interpretation

Authors:
Erik Palmgren
Affiliations:
Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden Email: palmgren@math.uu.se
Venue:
Mathematical Structures in Computer Science
Year:
2004

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Abstract

In this paper we interpret (fragments of) intuitionistic logic in categories with weak closure properties, such as quasi left exact categories and locally cartesian closed categories (LCCC) with sums. We also interpret the full choice scheme in an LCCC. The interpretation can be seen as a categorical form of the usual Brouwer–Heyting– Kolmogorov (BHK) interpretation. The standard interpretation of geometric logic in a pretopos is obtained by applying the image functor to the BHK-interpretation.