The advance of Ubiquitous Computing (UbiComp) and Internet of Things (IoT) brought a new set of Non-Functional Requirements (NFRs), especially related to Human-Computer Interaction (HCI). Invisibility is one of these NFRs, and it refers to either the merging of technology in the user environment or the decrease of the interaction workload. This new NFR may impact traditional NFRs (e.g., Usability), revealing positive correlations, when one NFR helps another, and negative correlations, when a procedure favors an NFR but creates difficulty for another one. Software engineers need to know about these correlations, so they can select appropriate strategies to satisfy Invisibility and traditional NFRs. Correlations between NFRs are usually stored in catalogs, which is a well-defined body of knowledge gathered from previous experience. Although Invisibility has been recently cataloged with development strategies, the literature still lacks catalogs with correlations for this NFR. Therefore, this work aims at capturing and cataloging invisibility correlations for UbiComp and IoT systems. To do that, we also propose to systematize the definition of correlations using the following well-defined research methods: Interview, Content Analysis and Questionnaire. As a result, we defined a catalog with 110 positive and negative correlations with 9 NFRs. This well-defined body of knowledge is useful for supporting software engineers to select strategies to satisfy Invisibility and other NFRs related to user interaction.