Definition df-bj-topmgmhom 37142

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 37141	. 2 class TopMgm⟶
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		ctmd 23978	. . 3 class TopMnd
5	2	cv 1540	. . . . 5 class 𝑥
6	3	cv 1540	. . . . 5 class 𝑦
7		ctophom 37137	. . . . 5 class Top⟶
8	5, 6, 7	co 7341	. . . 4 class (𝑥 Top⟶ 𝑦)
9		cmgmhom 37139	. . . . 5 class Mgm⟶
10	5, 6, 9	co 7341	. . . 4 class (𝑥 Mgm⟶ 𝑦)
11	8, 10	cin 3899	. . 3 class ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦))
12	2, 3, 4, 4, 11	cmpo 7343	. 2 class (𝑥 ∈ TopMnd, 𝑦 ∈ TopMnd ↦ ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦)))
13	1, 12	wceq 1541	1 wff TopMgm⟶ = (𝑥 ∈ TopMnd, 𝑦 ∈ TopMnd ↦ ((𝑥 Top⟶ 𝑦) ∩ (𝑥 Mgm⟶ 𝑦)))

This definition is referenced by: (None)