Abstract
Let be the homotopy category of a stable infinity category . Then the homotopy category of morphisms in the stable infinity category is also triangulated. Hence, the space of stability conditions on is well-defined though the nonemptiness of is not obvious. Our basic motivation is a comparison of the homotopy type of and that of . Under the motivation, we show that functors and induce continuous maps from to contravariantly where (resp., ) takes a morphism to the target (resp., source) of the morphism. As a consequence, if is nonempty, then so is . Assuming is the derived infinity category of the projective line over a field, we further study basic properties of and . In addition, we give an example of a derived category which does not have any stability condition.
Citation
Kotaro Kawatani. "Stability conditions on morphisms in a category." Kyoto J. Math. 62 (3) 485 - 521, September 2022. https://doi.org/10.1215/21562261-2022-0014
Information