Search Results

I don't think this is completely standard, so if I were going to use it I would explain it first, but a natural possibility is "$\mathcal{F}$-isomorphism" (-monomorphism, -epimorphism). Quasi-isomo …

In Sketches of an Elephant this kind of morphism is called a cover (section A1.3). In case you don't like that, here are some other possibilities (although I don't know that I actually like any of the …

As Peter said in a comment, "objectwise" is quite common and would probably be understood even without quotation marks, although it never hurts to define a term the first time you use it. I expect th …

Zhen is right that you can think of it as a lax monoidal pseudofunctor. In this paper, I called an equivalent structure a "monoidal fibration".

One name that I have seen used is semiadditive category.

This is the Cauchy completion of $\mathcal{C}$ as an $\mathrm{Ab}$-enriched category.

Of course, as Finn pointed out, there is controversy over the choice for natural transformations, but my views on that are clear at the nlab page so I'll just write using that terminology. …

In May's paper The additivity of traces in triangulated categories he has the following things to say about this property. (At least, I think it is an equivalent property -- his notation is different …

I think one name for this is a simulation.

(Indeed, in this case we have "$C = M\circ E$" as monads in $\rm Prof$ via a distributive law, as shown by Cheng --- this long postdates the terminology, but the underlying intuition was probably there …

I would call those objects "codiscrete" or "co-0-truncated", since "discrete" and "0-truncated" are used for the dual property, e.g. here and here. It's equivalent to saying that $B$ is equivalent to …