nLab objective number theory

Idea

Objective number theory is the study of addition and multiplication (and eventually exponentiation) of objects in suitable categories. (Stephen Schanuel 2000, p.295)

Related entries

• number theory

• extensive category

• distributive category

• Burnside rig

• polynomial functor

• FinSet

• decategorification

References

• John Baez, James Dolan, From finite sets to Feynman diagrams , pp.29-50 in Engquist, Schmid (eds.), Mathematics Unlimited - 2001 and Beyond , Springer Heidelberg 2001.

• Andreas Blass, Seven trees in one, Journal of Pure and Applied Algebra, 103 1 (1995) 1–21 [arXiv:math/9405205, doi:10.1016/0022-4049(95)00098-H]

• Marcelo Fiore, Tom Leinster, An Objective Representation of the Gaussian Integers , J. Symbolic Computation 37 no.6 (2004) pp.707-716. (arXiv)

• Marcelo Fiore, Tom Leinster, Objects of categories as complex numbers, Advances in Mathematics 190 (2005) pp.264-277. (arXiv)

• Robbie Gates, On the generic solution to $P(X)\simeq X$ in distributive categories , JPAA 125 (1998) pp.191-212.

• Robbie Gates, On generic seperable objects , TAC 4 no.10 pp.208-248 (1998). (abstract)

• F. William Lawvere, Qualitative Distinctions between some Toposes of Generalized Graphs , Cont. Math. 92 (1989) pp.261-299.

• Matías Menni, Every Rig with a One-Variable Fixed Point Presentation is the Burnside Rig of a Prextensive Category , Appl. Cat. Struc. 25 (2017) pp.663-707.

• Stephen Schanuel, Negative sets have Euler characteristic and dimension , Category theory. Proc. Int. Conf. Como/Italy 1990, LNM 1488 pp.379–385 (1991).

• Stephen Schanuel, Objective number theory and the retract chain condition , JPAA 154 pp.295–298 (2000).

• Stephen Schanuel, Transcendence in objective number theory , in Categorical studies in Italy, Perugia 1997. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 43–48, 64 (2000).