Definition df-bj-topmgmhom 36641

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 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦)))

Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-bj-topmgmhom

Step	Hyp	Ref	Expression
1		ctopmgmhom 36640	. 2 class TopMgm⟶
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		ctmd 23994	. . 3 class TopMnd
5	2	cv 1532	. . . . 5 class 𝑥
6	3	cv 1532	. . . . 5 class 𝑦
7		ctophom 36636	. . . . 5 class Top⟶
8	5, 6, 7	co 7426	. . . 4 class (𝑥 Top⟶ 𝑦)
9		cmgmhom 36638	. . . . 5 class Mgm⟶
10	5, 6, 9	co 7426	. . . 4 class (𝑥 Mgm⟶ 𝑦)
11	8, 10	cin 3948	. . 3 class ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦))
12	2, 3, 4, 4, 11	cmpo 7428	. 2 class (𝑥 ∈ TopMnd, 𝑦 ∈ TopMnd ↦ ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦)))
13	1, 12	wceq 1533	1 wff TopMgm⟶ = (𝑥 ∈ TopMnd, 𝑦 ∈ TopMnd ↦ ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦)))

This definition is referenced by: (None)