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Complete topos implies cocomplete - #444
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ScriptRaccoon merged 3 commits intoOct 30, 2026
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…e shape -> colimits of opposite shape
ScriptRaccoon
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Oct 29, 2026
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Thanks for the PR. The changes are OK, I just have 4 minor comments. |
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OK, I've addressed the comments in terms of grouping by limit type instead of by cardinalities, and adding some missing entries. I also added a few other missing entries I noticed while scanning the property list (regarding wide pullbacks and connected limits). I'll let you decide which ones you think are redundant, if any. |
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Co-authored-by: Daniel Schepler <11821574+dschepler@users.noreply.github.com>
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This adds several corollaries of the fact that in an elementary topos, the power object functor$T^{op} \to T$ is monadic and therefore creates limits, i.e. it creates colimits in T from limits in T. It came up in #362 as a convenient way to prove that since the effective topos doesn't have countable copowers, it also doesn't have countable powers.