nLab
objective number theory

Context

Category Theory

Arithmetic

Idea

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

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 , JPAA 103 no.1 (1995) pp.1–21.

  • 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)XP(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).

Last revised on December 12, 2020 at 17:19:25. See the history of this page for a list of all contributions to it.