Complete internal categories
Category Theory
2020-04-21 v1
Abstract
Internal categories feature notions of limit and completeness, as originally proposed in the context of the effective topos. This paper sets out the theory of internal completeness in a general context, spelling out the details of the definitions of limit and completeness and clarifying some subtleties. Remarkably, complete internal categories are also cocomplete and feature a suitable version of the adjoint functor theorem. Such results are understood as consequences of the intrinsic smallness of internal categories.
Cite
@article{arxiv.2004.08741,
title = {Complete internal categories},
author = {Enrico Ghiorzi},
journal= {arXiv preprint arXiv:2004.08741},
year = {2020}
}
Comments
33 pages