This appeal is from a preliminary injunction staying a demand for the arbitration of a contract dispute between • the parties. Appellant, Algernon Blair, Inc., is the general contractor hired by appellee, the City of Meridian, Mississippi, to construct a wastewater treatment plant. The contract between the parties contained a provision that disputes arising thereunder would be resolved by arbitration. Upon the City’s suit asking for declaratory and injunctive relief from a demand for arbitration by Blair, the district court granted an injunction on the ground that the particular dispute was not covered by the contract requirement. We reverse and direct that a stay pending arbitration of the dispute be entered.
Under the contract between the parties, the contractor, Blair, was required to subcontract the Instrumentation, Control and Monitoring System (ICMS) to a “qualified ICMS supplier.” The contract provided: “The many references made herein to work requirements and responsibilities of the ICM supplier shall only mean that responsibilities shall pass through the ICM supplier but in the final analysis shall rest with the contractor.” Blair subcontracted the ICMS work to Johnson Controls.
During the course of the work on the plant, Johnson claimed that the City had expanded the scope of its work requirements beyond those set out in the original specifications. Johnson filed a request for a change order to its contract and claimed an additional $105,787 to compensate for the added labor and materials expended. Blair claimed its usual markup for overhead and administrative expenses and submitted a request for $128,002.27 to the City for payment. The City refused to pay this change order request. Blair then filed a demand for arbitration with the American Arbitration Association against the City “for the use and benefit of Johnson.” The City obtained a temporary restraining order in state court, enjoining Blair from pursuing its arbitration demand on the ground the claim was Johnson’s and not Blair’s. Blair removed the case to federal court and moved to stay litigation pending arbitration. The City moved to stay arbitration *527pending litigation. The district judge entered a preliminary injunction staying the arbitration. Blair and Johnson appeal. The City moved to dismiss the appeal for lack of jurisdiction. A panel of this Court ordered the City’s motion to dismiss carried with the case.
I. Appealable Order
Before addressing the arbitrability issue, we first respond to the City’s motion to dismiss the appeal as not falling within the jurisdictional grant of authority under 28 U.S.C. § 1292(a)(1) authorizing appeal of interlocutory injunctive orders. The City supports its motion by reference to decisions in the Second Circuit which hold that orders staying arbitration pending the outcome of litigation do not fall within the scope of the statutory requirement. See AAACON Auto Transport, Inc. v. Ninfo, 490 F.2d 83 (2d Cir.1974); Diematic Mfg. Gorp. v. Packaging Industries, Inc., 516 F.2d 975 (2d Cir.), cert. denied, 423 U.S. 913, 96 S.Ct. 217, 46 L.Ed.2d 141 (1975). In the Fifth Circuit, however, the law on this point has already been decisively established to the contrary. In Texaco, Inc. v. American Trading Transportation Co., 644 F.2d 1152 (5th Cir.1981), this Court noted the lack of uniformity among the circuits but nevertheless firmly held that “an order granting a stay of arbitration pending outcome of litigation is an appealable interlocutory order under 28 U.S.C. § 1292(a)(1).” We follow this established law. The City’s motion to dismiss the appeal is denied.
II. Injunction
The decision to grant or deny a preliminary injunction is discretionary with the trial court and may be reversed on appeal only by a showing of abuse of discretion. See Doran v. Salem Inn, 422 U.S. 922, 95 S.Ct. 2561, 2568, 45 L.Ed.2d 648 (1975); Wilson v. Thompson, 593 F.2d 1375, 1384 (5th Cir.1979). The four prerequisites for granting a preliminary injunction were set out by this Court in Canal Authority of the State of Florida v. Callaway, 489 F.2d 567, 572 (5th Cir.1974). In order to secure an injunction, the movant must show:
(1) [A] substantial likelihood that plaintiff will prevail on the merits, (2) a substantial threat that plaintiff will suffer irreparable injury if the injunction is not granted, (3) that the threatened injury to plaintiff outweighs the threatened harm the injunction may do to defendant, and (4) that granting the preliminary injunction will not disserve the public interest.
The district court in the present case concluded that the City had carried the burden of proof with respect to these four factors. The predominant factor in the district court’s decision was its prediction that the City would prevail on the merits. In order to prevail on the merits, however, the City had to show that Blair’s claim was not arbitrable. We find that the claim is arbi-trable, and for this reason, reverse the injunction below.
III. Arbitrability
Both parties agree that the disputed contract involves interstate commerce and thus falls within the meaning of the Federal Arbitration Act, 9 U.S.C. §§ 1 et seq.1 The Act “is a congressional declaration of a liberal federal policy favoring arbitration agreements...” Moses H. Cone Memorial Hospital v. Mercury Construction Corp., — U.S. —, 103 S.Ct. 927, 941, 74 L.Ed.2d 765 (1983). Whenever the scope of an arbitration clause is in question, the court should construe the clause in favor of arbitration.2 United Steelworkers v. Warrior & Gulf Nav. Co., 363 U.S. 574, 80 S.Ct. 1347, 1353, 4 L.Ed.2d 1409 (1960). “[T]he courts of appeals have ... consistently concluded that questions of arbitrability must be addressed with a healthy regard for the federal policy favoring arbitration. . .. The Arbitration Act establishes that, as a matter of federal law, any doubts concerning the scope of arbitrable issues should be *528resolved in favor of arbitration, whether the problem at hand is the construction of the contract language itself or an allegation of waiver, delay or a like defense to arbitra-bility.” Moses H. Cone Memorial Hospital, supra, 103 S.Ct. at 941-42.
In addition to establishing a strong presumption in favor of arbitration, the Act also limits the role of the court in determining whether an issue is arbitrable. The court’s sole function is to determine whether the claim is referable to arbitration. Once that determination is made, the court may not delve further into the dispute.3 “The courts ... have no business weighing the merits of the grievance, considering whether there is equity in a particular claim, or determining whether there is particular language in the written instrument which will support the claim.” United Steelworkers of America v. American Manufacturing Co., 363 U.S. 564, 80 S.Ct. 1343, 1346, 4 L.Ed.2d 1403 (1960). Blair is making a claim. Whether the claim is valid or not is for the arbitrator to decide.
The arbitration clause in the Blair/City of Meridian contract read as follows:
All claims, disputes and other matters in question arising out of, or relating to, the CONTRACT DOCUMENTS or the breach thereof, except for claims which have been waived by the making and acceptance of final payment as provided by Section 20, shall be decided by arbitration in accordance with the Construction Industry Arbitration Rules of the American Arbitration Association. The decision to arbitrate shall be specifically enforceable under the prevailing arbitration law. The award rendered by the arbitrators shall be final, and judgment may be entered upon in any court having jurisdiction thereof.
Despite the broad scope of this arbitration clause, the City argues that it is not bound to arbitrate. The City does not contest the fact that the subject matter of the dispute fell within the scope of the arbitration clause. On the contrary, the City admits in its complaint that the work which formed the subject matter of the demand for arbitration was included in the original contract. Neither does the City contest the fact that Blair had a right to compel arbitration as to its claims under the clause. The City admits, as it must, that it looks to Blair for complete performance of the contract. The obligation under the contract is Blair’s — not Johnson’s. The City even concedes that if Johnson makes its claim against Blair and Blair is ultimately found liable to Johnson in that proceeding, Blair would have the right to force the City to arbitrate the issue. The City’s only claim is that it should not be forced to arbitrate what it asserts is a dispute between Johnson and Blair because Blair has not yet been held liable for the disputed costs or even admitted liability for additional sums under the contract. In short, the City balks at arbitration because it does not feel Blair has stated a claim of its own.
It is true that Blair may have to pay some of its recovery from arbitration to Johnson pursuant to another contract, but that is irrelevant to the resolution of this case. The fact that Johnson may have a claim against Blair under the Blair-Johnson contract does not deprive Blair of the right to arbitrate any claim against the City that is covered by the City-Blair contract. Blair has made a claim against the City under its contract, and the contract provides for arbitration of this dispute. The arrangement between Blair and Johnson is not the concern of the City. The City looks wholly to Blair for the carrying out and completion of the entire project including all of the subcontracted work.
Even if Blair does not have what we consider to be a valid substantive claim, the *529courts do not have the authority to enjoin arbitration on that ground. That is for the arbitrator to decide. Once we determine that the subject matter of the dispute is covered by the arbitration clause and that the party initiating arbitration is covered by the clause, we must allow the matter to be submitted to arbitration. Our sole function is to determine whether arbitration should be commenced; we play no part in determining the strength of claims and defenses presented. The City’s objection in this case is that Blair cannot recover for Johnson’s claim. We have no right to assume the arbitrator will deal incorrectly with the issue of whether this is Blair’s or Johnson’s claim under the City-Blair contract. In making the decision to enjoin arbitration, the district court relied predominantly on its conclusion that Blair had not yet been made liable or damaged in any way. That conclusion went beyond the power of the district court because it implicated the merits of the dispute.
The district court also gave summary attention to the other three factors typically used to justify preliminary injunctions. For one, the district court found that the City would suffer irreparable injury if Blair were allowed to proceed to arbitration. We disagree. Even if the parties were ordered to begin arbitration, the City could continue to challenge the claim to the arbitrator and to the courts if there was an unfavorable decision. If a legal challenge proved successful, the City obviously would not be bound by the findings or conclusions of the arbitrator. Although the City may have to suffer the expense of inappropriate arbitration, such expenditures do not constitute irreparable harm. “An injury is ‘irreparable’ only if it cannot be undone through monetary remedies.” Deerfield Medical Center v. City of Deerfield Beach, 661 F.2d 328, 338 (5th Cir.1981).
We also disagree with the district court’s conclusion that the injunction would not harm Blair or disserve the public interest. In contrast with the City, Blair does stand to suffer irreparable harm. Even if Blair ultimately wins in court and the issue returns to arbitration, the expense and delay of court action will deprive Blair of a significant portion of its bargain. Since swift and less costly resolution of disputes is the primary reason for an agreement to arbitrate, an injunction against arbitration can cause irreparable harm. That is a major reason why injunctions staying arbitrations are viewed with disfavor.
Finally, in light of the strong federal policy favoring arbitration over litigation, 9 U.S.C. §§ 1 et seq., we find that the public interest would be thwarted by an injunction against arbitration on these facts. See, Seaboard Coast Line Railroad Co. v. National Rail Passenger Corp., 554 F.2d 657, 660 (5th Cir.1977).
In sum, we are unable to find any basis for the issuance of a preliminary injunction. Although the grant or denial of injunctive relief pending a trial on the merits is a decision within the discretion of the district court, we find that on the record in this case, the issuance of an injunction constituted an abuse of judicial discretion. Accordingly, we vacate the district court order granting a preliminary injunction and direct that a stay pending arbitration of the dispute be entered.
REVERSED.