-
Recent Posts
Blogroll
Archives
Tags
- ac.commutative-algebra
- ag.algebraic-geometry
- ap.analysis-of-pdes
- at.algebraic-topology
- co.combinatorics
- ct.category-theory
- cv.complex-variables
- dg.differential-geometry
- fa.functional-analysis
- field-theory
- general-topology
- geometric-topology
- gr.group-theory
- harmonic-analysis
- lie-algebras
- lie-groups
- linear-algebra
- measure-theory
- metric-spaces
- nt.number-theory
- polynomials
- ra.rings-and-algebras
- rewriting-systems
- rt.representation-theory
- vector-bundles
Tag Archives: ct.category-theory
The categorical product’s natural maps aren’t necessarily epimorphisms
Consider the following category: subject to the relation . Then is the product of and , since it (vacuously) verifies the universal property, but is not an epimorphism. Dually, one gets that the coproduct’s natural maps aren’t monomorphisms in general.