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Dec 10, 2017 at 22:17 vote accept John Berman
Dec 10, 2017 at 22:03 comment added Karol Szumiło If you don't include terminal objects, then I agree that coproducts and filtered colimits are preserved. I don't believe this is the case for pushouts though.
Dec 10, 2017 at 17:45 comment added John Berman To be clear, LCC categories need not have terminal objects, at least for me, so the empty category is LCC.
Dec 10, 2017 at 15:02 comment added John Berman Thank you! I will take a look at that paper, but this should be what I am looking for. I do think that the initial LCC category is empty, and that the forgetful functor at least preserves coproducts and filtered colimits.
Dec 10, 2017 at 7:15 history answered Karol Szumiło CC BY-SA 3.0