Definition df-bj-topmgmhom 37812

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 37811	. 2 class TopMgm⟶
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		ctmd 24264	. . 3 class TopMnd
5	2	cv 1569	. . . . 5 class 𝑥
6	3	cv 1569	. . . . 5 class 𝑦
7		ctophom 37807	. . . . 5 class Top⟶
8	5, 6, 7	co 7423	. . . 4 class (𝑥 Top⟶ 𝑦)
9		cmgmhom 37809	. . . . 5 class Mgm⟶
10	5, 6, 9	co 7423	. . . 4 class (𝑥 Mgm⟶ 𝑦)
11	8, 10	cin 3907	. . 3 class ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦))
12	2, 3, 4, 4, 11	cmpo 7425	. 2 class (𝑥 ∈ TopMnd, 𝑦 ∈ TopMnd ↦ ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦)))
13	1, 12	wceq 1570	1 wff TopMgm⟶ = (𝑥 ∈ TopMnd, 𝑦 ∈ TopMnd ↦ ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦)))

This definition is used by: (None)