Theory in Context, Dover, 2016, pointed-object examples

Emily Riehl, C. (2016). Theory in Context, Dover, 2016, pointed-object examples.

Type

Unclassified

Intellectual base

Unclassified

Year

2016

Link

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Cited by

4 citations across 4 artifacts.

Domain-specific

• Category of sets
  • … are injective functions, epimorphisms are surjective functions under ordinary choice-independent element arguments, and isomorphisms are bijections. to A forgetful functor from groups to Set retains underlying sets and functions, allowing algebraic constructions to be compared with their set-level carriers..
• Diagram (category theory)
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Pointed set
  • … and a convenient observable transfers from Adding a disjoint basepoint to an ordinary set produces X+={}⊔X, while a pointed map must send to the target's basepoint. to A based topological space forgets topology to a pointed set, retaining the reference point used for homotopy groups and wedge constructions..
• Twisted diagonal (category theory)
  • … source and target maps in a twisted morphism, commutative-square equation, identity and composition, category-of-elements formulation and simplicial or nerve generalization are explicit. to An applied instance preserves the invariant under changed notation, scale, dataset, jurisdiction, or implementation..

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