McCleary, Alexander J., authorPatel, Amit, advisorAdams, Henry, committee memberBen Hur, Asa, committee memberPeterson, Chris, committee member2021-09-062021-09-062021https://hdl.handle.net/10217/233845Persistent homology typically starts with a filtered chain complex and produces an invariant called the persistence diagram. This invariant summarizes where holes are born and die in the filtration. In the traditional setting the filtered chain complex is a chain complex of vector spaces filtered over a totally ordered set. There are two natural directions to generalize the persistence diagram: we can consider filtrations of more general chain complexes and filtrations over more general partially ordered sets. In this dissertation we develop both of these generalizations by defining persistence diagrams for chain complexes in an essentially small abelian category filtered over any finite lattice.born digitaldoctoral dissertationsengpersistent homologyapplied topologyTextThis material is open access and distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 United States License. (https://creativecommons.org/licenses/by-nc-nd/4.0).