ORBITS AND MONOIDS IN A TOPOS

[摘要] The linguistic intuition shows that many facts which are usually expressed in mathematics by using the explicit existence of a ''set of integers'', should be expressible without it. We make this intuition precise in the context of toposes (not necessarily) with a natural number object. This leads to the study of orbits of elements for endomaps X --> X in a topos. These can be identified with the monoids with one generator. We get results related to finiteness and existence of cyclic points, and study the fibration of the orbits.

[发布日期] 1994-02-18