dedekind::category::IsoRetract< F > Struct Template Reference

The retract of an IsIsomorphism: its total inverse arrow wrapped in an always-engaged std::optional. More...

Collaboration diagram for dedekind::category::IsoRetract< F >:

Public Member Functions
constexpr Maybe< Dom< F > >	operator() (const Cod< F > &y) const

Public Attributes
F	f

Detailed Description

template<typename F>
struct dedekind::category::IsoRetract< F >

The retract of an IsIsomorphism: its total inverse arrow wrapped in an always-engaged std::optional.

Every iso \(f:A\to B\) has a two-sided inverse \(f^{-1}:B\to A\), so its retract is total: retract(f)(y) is always Some(f^{-1}(y)), built through the maybe unit η(maybe_monad, ·) rather than a raw std::optional constructor. A named functor (not a lambda) so the type is nameable and the closure is transparent.

Template Parameters

F	The iso arrow type.

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The documentation for this struct was generated from the following file:

• src/main/modules/dedekind/category/iso.cppm