MathDBFree algebra existence in W-pretoposes with WISC
Free algebra existence in W-pretoposes with WISC
A W-pretopos is a category with the structural properties implicit in the paper, and WISC denotes the weak internal axiom of choice used there. Free algebra existence conjecture. Free algebras for varieties should exist in any W-pretopos that satisfies WISC. This would extend known existence results beyond the stronger choice assumptions used for general toposes; whether the construction can be obtained under weaker hypotheses remains open.
Sources & referencesView supporting material
Primary source
Andrew Swan, “W-Types with Reductions and the Small Object Argument”, arXiv:1802.07588 (2018).
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