The framework of this talk will be Causal Dynamical Triangulations, which is a lattice approach to quantum gravity. Using a discretized version of the Einstein-Hilbert action, CDT predicts the existence of a 4-dimensional deSitter spacetime. The lattice description allows for the incorporation of matter fields too, similarly as it is done for standard Lattice QCD. There is one caveat though, that is the nontrivial notion of dimension and topology. I will show what it means to have an effective description of spacetime dimension (DOI 10.1088/1361-6382/acd0fc) via the introduction of the discrete Laplacian operator and also show a phase-transition in topology using an interaction between scalar fields and the background geometry (DOI 10.1088/1361-6382/ac2135). Furthermore I will present results regarding the implementation of SU(N) Yang-Mills gauge fields and the topological charge as an observable (arXiv:2411.12668).