It's all in the title: Is there really no name for categories in which all automorphisms are trivial? I've encountered some examples of these, the most prominent being the simplex category.



Name for "Category without nontrivial automorphisms"?
To sum up the comments & discussion: no established terminology seems to exist, but *essentially gaunt* would be a good name for categories without nontrivial automorphisms.


For a related notion, categories without notrivial *isomorphisms* are called *gaunt*, see <https://ncatlab.org/nlab/show/gaunt+category>


On the other side, categories without nontrial *endomorphisms* are called *one-way*, and those without *infinite descending chains of non-id morphisms* are called *direct*, see <https://ncatlab.org/nlab/show/direct+category>


