Homotopy Type Theory H-magmoid > history (Rev #2, changes)

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Definition

An H-magmoid AA consists of the following.

  • A type A 0A_0, whose elements are called objects. Typically AA is coerced to A 0A_0 in order to write x:Ax:A for x:A 0x:A_0.

  • For each a,b:Aa,b:A, a type hom A(a,b)hom_A(a,b), whose elements are called arrows or morphisms.

  • For each a,b,c:Aa,b,c:A, a function

    hom A(b,c)hom A(a,b)hom A(a,c)hom_A(b,c) \to hom_A(a,b) \to hom_A(a,c)

    called composition, and denoted infix by gfgfg \mapsto f \mapsto g \circ f, or sometimes gfgf.

See also

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