Homotopy Type Theory extensional category > history (Rev #2, changes)

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Idea

An evaluational concrete category where morphisms satisfy the axiom of extensionality.

Definition

An extensional category CC is a evaluational concrete category such that for morphisms f:Hom(A,B)f:Hom(A,B) and g:Hom(A,B)g:Hom(A,B), if f(x)=g(x)f(x) = g(x) for all elements x:El(A)x:El(A), then f=gf = g.

Examples

  • The category SetSet of sets and functions is an extensional category.

  • The category MonMon of monoids and monoid homomorphisms is an extensional category.

  • The category Mod\mathbb{Z}Mod of $\mathbb{Z}$-modules and \mathbb{Z}-module homomorphisms is an extensional category.

  • The category Alg\mathbb{Z}Alg of $\mathbb{Z}$-algebras and \mathbb{Z}-algebra homomorphisms is an extensional category.

  • The category CRingCRing of commutative rings and commutative ring homomorphisms is an extensional category.

  • The category FieldField of fields and field homomorphisms is an extensional category.

  • The category HeytAlgHeytAlg of Heyting algebras and Heyting algebra homomorphisms is an extensional category.

  • The category FrmFrm of frames and frame homomorphisms is an extensional category.

  • The category ConvConv of set-truncated convergence spaces and continuous functions is an extensional category.

  • The category TopTop of set-truncated topological spaces and continuous functions is an extensional category.

  • The category of empty sets and functions is an extensional category.

See also

Revision on May 18, 2022 at 09:53:27 by Anonymous?. See the history of this page for a list of all contributions to it.