English

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.

Keywords

Cite

@article{arxiv.2004.08741,
  title  = {Complete internal categories},
  author = {Enrico Ghiorzi},
  journal= {arXiv preprint arXiv:2004.08741},
  year   = {2020}
}

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33 pages