Geodesic
Absolutely Free Algebras in a Topos Containing an Infinite Object
Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 323-328

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This note confirms that the existence proof for absolutely free algebras originated by Dedekind in [2] and completely developed for instance in [4] can still be carried out in a topos containing an infinite object i.e. an object N for which N ≃ N+1 if the type of the algebras considered is finite, pointed and internally projective i.e. is a finite sequence of objects, (I j )i≤j≤k for which the functors ( )I j preserve epimorphisms and each of which has a global section. 
Schumacher, D. Absolutely Free Algebras in a Topos Containing an Infinite Object. Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 323-328. doi: 10.4153/CMB-1976-049-5
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     title = {Absolutely {Free} {Algebras} in a {Topos} {Containing} an {Infinite} {Object}},
     journal = {Canadian mathematical bulletin},
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     year = {1976},
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     doi = {10.4153/CMB-1976-049-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-049-5/}
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