Dugger, DanielLester, Cynthia2019-09-182019-09-182019-09-18https://hdl.handle.net/1794/24924We explore the canonical Grothendieck topology and a new homotopical analog. First we discuss a specific description of the covers in the canonical topology, which we then use to get a corollary of Giraud's Theorem. Second we delve into the canonical topology on some specific categories, e.g. on the category of topological spaces and the category of abelian groups; this part includes concrete examples and non-examples. Lastly, we discuss a homotopical analog of the canonical Grothendieck topology and explore some examples of this analog.en-USAll Rights Reserved.colim sieveeffective epimorphismgeneralized sievehocolim sievehomotopical canonical topologyindex-functor categoryElectronic Thesis or Dissertation