query: Why is the trivial group a zero object for the category of groups, but the empty set isn't a zero object for the category of sets?
positive_passages.docid: 152354
positive_passages.text: Why is an empty set not a terminal object in categories $\mathsf{Top}$ and $\mathsf{Sets}$?
negative_passages.docid: 10679
negative_passages.text: Equivalence of Categories and of Their Functor Categories
negative_passages.docid: 119942
negative_passages.text: Standard argument for making the class group of a number field trivial
negative_passages.docid: 120557
negative_passages.text: Group of invertible elements of a ring has never order $5$
negative_passages.docid: 25039
negative_passages.text: Zero vector of a vector space
negative_passages.docid: 100716
negative_passages.text: Zero morphism does not depend on zero object
negative_passages.docid: 5022
negative_passages.text: Can a set containing $0$ be purely imaginary?
negative_passages.docid: 94727
negative_passages.text: When the trace of the Frobenius homomorphism is zero?
negative_passages.docid: 114320
negative_passages.text: Showing that if the center of a group is trivial, then the center of its automorphism group is trivial
negative_passages.docid: 80546
negative_passages.text: Why is closure omitted in some group definitions?
negative_passages.docid: 81406
negative_passages.text: Does every set have a group structure?
negative_passages.docid: 33767
negative_passages.text: Category of profinite groups
negative_passages.docid: 82315
negative_passages.text: is an empty set an element of {empty set}
negative_passages.docid: 109219
negative_passages.text: How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like?
negative_passages.docid: 88823
negative_passages.text: How can the empty set be open in the definition of the cofinite topology?
negative_passages.docid: 74978
negative_passages.text: How the center of a non-cyclic free Group is trivial?
negative_passages.docid: 1162
negative_passages.text: Why $\{\mathbf{0}\}$ has dimension zero?