Building globally-inclusive generative artificial intelligence (genAI) that encodes, respects, and valorizes cultural sensibilities as well as performs well for users across cultural contexts, is an important goal as we deploy generative AI products globally. If we are to build such inclusive AI for people, we must both have a better understanding of how we can make our AI pipeline more globally inclusive and how AI technologies can impact or shape cultures it is deployed in. If unexamined, this relationship between AI and culture will universalize western-centered AI and have unforeseen impacts on global cultural production, values and consumptions. However, this is not a relationship AI scholarship can understand on its own. We need an engagement with existing theories on the interplay between technology and culture, and how both can shape each other. We urgently thus need a cross-disciplinary and cross-community framework for understanding this multifaceted relationship between AI and Culture. This workshop aims to begin a conversation between core AI researchers and experts from the social sciences and humanities with a focus on the impact of generative AI on cultures and the cultural exclusions embedded in our on generative AI pipelines. Through this focus, the workshop will encourage field building on deepening our understanding for how we can build and deploy globally inclusive genAI and how we can responsibly encode cultural knowledge into our technologies.