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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Cohn, P. M., Universal Algebra, Harper and Row, 1965. Google Scholar

[2] 2. Dedekind, R., Was sind und was sollen die Zahlen? 1871. Google Scholar

[3] 3. Freyd, P., Aspects of topoi, Bull. Austral. Math. Soc, Vol. 7 (1972), p. 1–76. Google Scholar

[4] 4. Kerkhoff, R., Eine Konstruktion freier Algebren, Math. Annalen, Vol. 158 (1965), p. 109–112. Google Scholar

[5] 5. Lesaflre, B., Structures algébriques dans les topos élémentaires, C. R. Acad. Se. Paris, t277 (8 octobre 1973), p. 663–666. Google Scholar

[6] 6. Mikkelsen, Ch. J., On the internal completeness of elementary topoi, Tagungsbericht 30/1973, Mathematisches Forschungsinstitut Oberwolfach. Google Scholar

[7] 7. Schumacher, D., Peanoalgebras in a topos containing a natural number object, Tagungsbericht 30/1973, Mathematisches Forschungsinstitut Oberwolfach. Google Scholar

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