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Definition df-bj-topmgmhom 36314
Description: Define the set of topological magma morphisms (continuous magma morphisms) between two topological magmas. If domain and codomain are topological semigroups, monoids, or groups, then one obtains the set of morphisms of these structures. This definition is currently stated with topological monoid domain and codomain, since topological magmas are currently not defined in set.mm. (Contributed by BJ, 10-Feb-2022.)
Assertion
Ref Expression
df-bj-topmgmhom TopMgm⟶ = (𝑥 ∈ TopMnd, 𝑦 ∈ TopMnd ↦ ((𝑥 Top𝑦) ∩ (𝑥 Mgm𝑦)))
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-bj-topmgmhom
StepHypRef Expression
1 ctopmgmhom 36313 . 2 class TopMgm
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 ctmd 23795 . . 3 class TopMnd
52cv 1539 . . . . 5 class 𝑥
63cv 1539 . . . . 5 class 𝑦
7 ctophom 36309 . . . . 5 class Top
85, 6, 7co 7412 . . . 4 class (𝑥 Top𝑦)
9 cmgmhom 36311 . . . . 5 class Mgm
105, 6, 9co 7412 . . . 4 class (𝑥 Mgm𝑦)
118, 10cin 3947 . . 3 class ((𝑥 Top𝑦) ∩ (𝑥 Mgm𝑦))
122, 3, 4, 4, 11cmpo 7414 . 2 class (𝑥 ∈ TopMnd, 𝑦 ∈ TopMnd ↦ ((𝑥 Top𝑦) ∩ (𝑥 Mgm𝑦)))
131, 12wceq 1540 1 wff TopMgm⟶ = (𝑥 ∈ TopMnd, 𝑦 ∈ TopMnd ↦ ((𝑥 Top𝑦) ∩ (𝑥 Mgm𝑦)))
Colors of variables: wff setvar class
This definition is referenced by: (None)
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