Roller, in particular a rigid or swivel caster, and a roller attached to a support

The invention relates, first of all, to a roller (1) or a roller (1) attached to a support (2), in particular a rigid or swivel caster, and having a running wheel (6) that has a running wheel axis (x) and is accommodated in a mounting fork (3), the mounting fork (3) forming an overlap portion (4) with regard to the running wheel (6) and a mounting part (17) being provided preferably in the overlap region (4) and preferably on the upper side, wherein, in addition, in a roller attached to a support, a counter mounting part (29) is attached to the support. In order to improve a roller of the type in question or a roller attached to a support in such a way that easy assembly with the support of a rollable object can be achieved, it is proposed that the mounting part (17) and/or a counter mounting part (29) is designed for sliding attachment. The invention also relates to such a roller (1) or a roller (1) attached to a support (2) in which an attachment pin (35) is provided on the upper side of the overlap region (4), said attachment pin extending in a vertical direction in an assembled state and being in the form of a cone that tapers in the direction of its free end.